writing summary

Measurement and Analysis of Online Social Networks

Alan Mislove MPI for Software Systems

Campus E1 4 Saarbrücken 66123, Germany

Massimiliano Marcon MPI for Software Systems

Campus E1 4 Saarbrücken 66123, Germany

Krishna P. Gummadi MPI for Software Systems

Campus E1 4 Saarbrücken 66123, Germany

Peter Druschel MPI for Software Systems

Campus E1 4 Saarbrücken 66123, Germany

Bobby Bhattacharjee Computer Science Department

University of Maryland College Park, MD 20742

ABSTRACT Online social networking sites like Orkut, YouTube, and Flickr are among the most popular sites on the Internet. Users of these sites form a social network, which provides a powerful means of sharing, organizing, and finding con- tent and contacts. The popularity of these sites provides an opportunity to study the characteristics of online social network graphs at large scale. Understanding these graphs is important, both to improve current systems and to design new applications of online social networks.

This paper presents a large-scale measurement study and analysis of the structure of multiple online social networks. We examine data gathered from four popular online social networks: Flickr, YouTube, LiveJournal, and Orkut. We crawled the publicly accessible user links on each site, ob- taining a large portion of each social network’s graph. Our data set contains over 11.3 million users and 328 million links. We believe that this is the first study to examine multiple online social networks at scale.

Our results confirm the power-law, small-world, and scale- free properties of online social networks. We observe that the indegree of user nodes tends to match the outdegree; that the networks contain a densely connected core of high-degree nodes; and that this core links small groups of strongly clus- tered, low-degree nodes at the fringes of the network. Fi- nally, we discuss the implications of these structural prop- erties for the design of social network based systems.

Categories and Subject Descriptors H.5.m [Information Interfaces and Presentation]: Mis- cellaneous; H.3.5 [Information Storage and Retrieval]: Online Information Services—Web-based services

General Terms Measurement

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Keywords Social networks, measurement, analysis

1. INTRODUCTION The Internet has spawned different types of information sharing systems, including the Web. Recently, online so- cial networks have gained significant popularity and are now among the most popular sites on the Web [40]. For example, MySpace (over 190 million users1), Orkut (over 62 million), LinkedIn (over 11 million), and LiveJournal (over 5.5 mil- lion) are popular sites built on social networks.

Unlike the Web, which is largely organized around con- tent, online social networks are organized around users. Par- ticipating users join a network, publish their profile and any content, and create links to any other users with whom they associate. The resulting social network provides a basis for maintaining social relationships, for finding users with sim- ilar interests, and for locating content and knowledge that has been contributed or endorsed by other users.

An in-depth understanding of the graph structure of on- line social networks is necessary to evaluate current systems, to design future online social network based systems, and to understand the impact of online social networks on the Internet. For example, understanding the structure of on- line social networks might lead to algorithms that can de- tect trusted or influential users, much like the study of the Web graph led to the discovery of algorithms for finding au- thoritative sources in the Web [21]. Moreover, recent work has proposed the use of social networks to mitigate email spam [17], to improve Internet search [35], and to defend against Sybil attacks [55]. However, these systems have not yet been evaluated on real social networks at scale, and lit- tle is known to date on how to synthesize realistic social network graphs.

In this paper, we present a large-scale (11.3 million users, 328 million links) measurement study and analysis of the structure of four popular online social networks: Flickr, YouTube, LiveJournal, and Orkut. Data gathered from mul- tiple sites enables us to identify common structural proper- ties of online social networks. We believe that ours is the first study to examine multiple online social networks at scale. We obtained our data by crawling publicly accessible information on these sites, and we make the data available

1Number of distinct identities as reported by the respective sites in July 2007.

to the research community. In contrast, previous studies have generally relied on propreitary data obtained from the operators of a single large network [4].

In addition to validating the power-law, small-world and scale-free properties previously observed in offline social net- works, we provide insights into online social network struc- tures. We observe a high degree of reciprocity in directed user links, leading to a strong correlation between user inde- gree and outdegree. This differs from content graphs like the graph formed by Web hyperlinks, where the popular pages (authorities) and the pages with many references (hubs) are distinct. We find that online social networks contain a large, strongly connected core of high-degree nodes, surrounded by many small clusters of low-degree nodes. This suggests that high-degree nodes in the core are critical for the connectivity and the flow of information in these networks.

The focus of our work is the social network users within the sites we study. More specifically, we study the properties of the large weakly connected component2 (WCC) in the user graphs of four popular sites. We do not attempt to study the entire user community (which would include users who do not use the social networking features), information flow, workload, or evolution of online social networking sites. While these topics are important, they are beyond the scope of this paper.

The rest of this paper is organized as follows: We provide additional background on social networks in Section 2 and detail related work in Section 3. We describe our methodol- ogy for crawling these networks, and its limitations, in Sec- tion 4. We examine structural properties of the networks in Section 5, and discuss the implications in Section 6. Finally, we conclude in Section 7.

2. BACKGROUND AND MOTIVATION We begin with a brief overview of online social networks. We then describe a simple experiment we conducted to estimate how often the links between users are used to locate content in a social networking site like Flickr. Finally, we discuss the importance of understanding the structure of online social networks.

Online social networks have existed since the beginning of the Internet. For instance, the graph formed by email users who exchange messages with each other forms an online so- cial network. However, it has been difficult to study this network at large scale due to its distributed nature.

Popular online social networking sites like Flickr, You- Tube, Orkut, and LiveJournal rely on an explicit user graph to organize, locate, and share content as well as contacts. In many of these sites, links between users are public and can be crawled automatically to capture and study a large fraction of the connected user graph. These sites present an opportunity to measure and study online social networks at a large scale.

2.1 Online social networking sites Online social networking sites are usually run by individual corporations (e.g. Google and Yahoo!), and are accessible via the Web.

2A weakly connected component in a directed graph is a set of nodes where each node in the set has a path to every other node in the set if all links are viewed as undirected.

Users. To participate fully in an online social network, users must register with a site, possibly under a pseudonym.3

Some sites allow browsing of public data without explicit sign-up. Users may volunteer information about themselves (e.g., their birthday, place of residence, or interests), which is added to the user’s profile.

Links. The social network is composed of user accounts and links between users. Some sites (e.g. Flickr, LiveJournal) allow users to link to any other user, without consent from the link target. Other sites (e.g. Orkut, LinkedIn) require consent from both the creator and target before a link is created connecting these users.

Users form links for one of several reasons. The nodes connected by a link can be real-world acquaintances, online acquaintances, or business contacts; they can share an in- terest; or they can be interested in each other’s contributed content. Some users even see the acquisition of many links as a goal in itself [14]. User links in social networks can serve the purpose of both hyperlinks and bookmarks in the Web.

A user’s links, along with her profile, are visible to those who visit the user’s account. Thus, users are able to explore the social network by following user-to-user links, brows- ing the profile information and any contributed content of visited users as they go. Certain sites, such as LinkedIn, only allow a user to browse other user accounts within her neighborhood (i.e. a user can only view other users that are within two hops in the social network); other sites, includ- ing the ones we study, allow users to view any other user account in the system.

Groups. Most sites enable users to create and join special interest groups. Users can post messages to groups and up- load shared content to the group. Certain groups are mod- erated; admission to such a group and postings to a group are controlled by a user designated as the group’s modera- tor. Other groups are unrestricted, allowing any member to join and post messages or content.

2.1.1 Is the social network used in locating content? Of the four popular social networking sites we study in this paper, only Orkut is a “pure” social networking site, in the sense that the primary purpose of the site is finding and con- necting to new users. Others are intended primarily for pub- lishing, organizing, and locating content; Flickr, YouTube, and LiveJournal are used for sharing photographs, videos, and blogs, respectively.

To investigate the role played by the social network in or- ganizing and locating content, we conducted a simple mea- surement of how users browse the Flickr system. We ana- lyzed the HTTP requests going to the flickr.com domain from a 55-day HTTP trace taken at the border routers of the Technical University of Munich between August 17th, 2006 and October 11th, 2006. We found 22,215 photo views from at least 1,056 distinct users. For each of these views, we examined the browser’s click stream to determine what action led the user to a given photo.

We found that 17,897 of the views (80.6%) resulted ei- ther from following links in the Flickr user graph or were

3In the rest of this paper, we use the term “user” to de- note a single unique identity in a social network. A person may create multiple identities, and may even create links be- tween these identities. We consider each of these identities as separate users.

additional views within a visited user’s collection. In other words, in 80.6% of the views, the user network was involved in browsing content. We count these views as being influ- enced by the social network. Focusing on the remaining views, 1,418 (6.3%) views were the result of using the Flickr photo search facilities. The remaining 2,900 (13.1%) views were the result of a link from an external source, such as links from an external site or links received via email. Nei- ther of the latter sets of views involved the social network.

Our experiment suggests that the social network in Flickr plays an important role in locating content. Four out of five photos were located by traversing the social network links.

2.2 Why study social networks? Online social networks are already at the heart of some very popular Web sites. As the technology matures, more ap- plications are likely to emerge. It is also likely that social networking will play an important role in future personal and commercial online interaction, as well as the location and organization of information and knowledge. Examples include browser plug-ins to discover information viewed by friends [39, 50], and social network based, cooperative Web search tools [35]. Even major Web search companies are de- ploying services that leverage social networks, like Yahoo!’s MyWeb 2.0 [54] and Google Co-op [19].

Below, we outline a few of the ways is which an under- standing of the structure of online social networks can ben- efit the design of new systems and help us understand the impact of online social networks on the future Internet. Ad- ditionally, we speculate how our data might be of interest to researchers in other disciplines.

2.2.1 Shared interest and trust Adjacent users in a social network tend to trust each other. A number of research systems have been proposed to ex- ploit this trust. SybilGuard [55] uses a social network to detect Sybil attacks in distributed systems, leveraging the fact that Sybil users will not be able to create many trust links to non-Sybil users. Re [17] exploits the trust between email users to aid spam classification by whitelisting mes- sages from friends and friends-of-friends. We believe that a deeper understanding of the underlying topology is an es- sential first step in the design and analysis of robust trust and reputation metrics for these systems.

Adjacent users in a social network also tend to have com- mon interests. Users browse neighboring regions of their social network because they are likely to find content that is of interest to them. Systems such as Yahoo! My Web [54], Google Co-op [19], and PeerSpective [35] use social networks to rank Internet search results relative to the interests of a user’s neighborhood in the social network. These sys- tems observe content viewed and search results clicked on by members of a social network in order to better rank the results of the user’s future searches.

Understanding the structure of online social networks, as well as the processes that shape them, is important for these applications. It would be useful to have efficient algorithms to infer the actual degree of shared interest between two users, or the reliability of a user (as perceived by other users). With respect to security, it is important to under- stand the robustness of such networks to deliberate attempts of manipulation. These topics are beyond the scope of this paper; however, a fundamental understanding of online so-

cial network structure is likely to be a necessary first step in these directions.

2.2.2 Impact on future Internet The social networks we study in this paper exist in the databases of online social networking sites. However, other online social networks are implemented as overlay networks. For instance, the graph formed by people who exchange email, or the graph formed by Skype [49] users who include each other in their contact lists can be viewed as another social network on top of the Internet. If future distributed online social networks are popular and bandwidth-intensive, they can have a significant impact on Internet traffic, just as current peer-to-peer content distribution networks do. Un- derstanding the structure of online social networks is not only critical to understanding the robustness and security of distributed online social networks, but also to understanding their impact on the future Internet.

2.2.3 Impact on other disciplines Additionally, our work has relevance beyond computer sci- ence. To social scientists, online social networks offer an un- precedented opportunity to study social networks at a large scale. Sociologists can examine our data to test existing the- ories about offline social networks, as well as to look for new forms of behavior in online social networks.

Studying the structure of online social networks may help improve the understanding of online campaigning and viral marketing. Political campaigns have realized the importance of blogs in elections [47]. Similarly, marketing experts are experimenting with paid viral marketing [44] to better pro- mote products and companies. Regardless of one’s stance on these phenomena, a better understanding of the structure of social networks is likely to improve our understanding of the opportunities, limitations, and threats associated with these ideas.

3. RELATED WORK In this section we describe studies of social networks, in- formation networks, as well as work on complex network theory.

3.1 Social networks Sociologists have studied many of the properties of social networks. Milgram [34] shows that the average path length between two Americans is 6 hops, and Pool and Kochen [46] provide an analysis of the small-world effect. The influential paper by Granovetter [20] argues that a social network can be partitioned into ‘strong’ and ‘weak’ ties, and that the strong ties are tightly clustered. For an overview of social network analysis techniques, we refer the reader to the book by Wasserman and Faust [51].

As online social networks are gaining popularity, sociol- ogists and computer scientists are beginning to investigate their properties. Adamic et al. [3] study an early online social network at Stanford University, and find that the net- work exhibits small-world behavior, as well as significant local clustering. Liben-Nowell et al. [32] find a strong cor- relation between friendship and geographic location in so- cial networks by using data from LiveJournal. Kumar et al. [26] examine two online social networks and find that both possess a large strongly connected component. Girvan and Newman observe that users in online social networks

tend to form tightly knit groups [18]. Backstrom et al. [8] examine snapshots of group membership in LiveJournal, and present models for the growth of user groups over time. We were able to verify these properties on a much larger scale.

In recent work, Ahn et al. [4] analyze complete data from a large South Korean social networking site (Cyworld), along with data from small sample crawls of MySpace and Orkut. The authors obtained data directly from CyWorld opera- tors, and the volume of available data allows the authors to conduct an in-depth study of that site using some of the same metrics that we use in this paper. The comparison with different networks, on the other hand, is limited by the small crawled data samples of MySpace and Orkut. Our study is largely complementary: the data available to us for any one site is less detailed, but we are able to compare large crawled data sets from multiple sites.

3.2 Information networks A long thread of research examines the structure of com- plex networks like the Web and the Internet. A prominent study of the Web link structure [12] shows that the Web has a “bow-tie” shape, consisting of a single large strongly con- nected component4 (SCC), and other groups of nodes that can either reach the SCC or can be reached from the SCC. We show that online social networks have a similar large component, but that its relative size is much larger than that of the Web’s SCC. Faloutsos et al. [16] show that the degree distribution of the Internet follows a power-law, and Siganos et al. demonstrate that the high-level structure of the Internet resembles a “jellyfish” [48].

Kleinberg [24] demonstrates that high-degree pages in the Web can be identified by their function as either hubs (con- taining useful references on a subject) or authorities (con- taining relevant information on a subject). Kleinberg also presents an algorithm [21] for inferring which pages function as hubs and which as authorities. The well-known PageRank algorithm [43] uses the Web structure to determine pages that contain authoritative information.

3.3 Complex network theory There has been much theoretical work on the properties of various classes of complex graphs.

Random networks have been extensively studied, starting with the seminal paper by Erdös and Réyni [15]. These graphs are usually constructed by randomly adding links to a static set of nodes. Researchers have shown that ran- dom graphs tend to have very short paths between any two nodes [25]. More recent work on random graphs has pro- vided mechanisms to construct graphs with specified degree distributions [36] and has characterized the size of the large connected component [37].

Power-law networks are networks where the probability that a node has degree k is proportional to k−γ , for large k and γ > 1. The parameter γ is called the power-law coef- ficient. Researchers have shown that many real-world net- works are power-law networks, including Internet topolo- gies [16], the Web [9, 27], social networks [3], neural net- works [11], and power grids [45].

Scale-free networks are a class of power-law networks where the high-degree nodes tend to be connected to other high-

4A strongly connected component in a graph is a set of nodes where each node in the set has a path to every other node in the set.

degree nodes. Scale-free graphs are discussed in detail by Li et al. [31], and they propose a metric to measure the scale- freeness of graphs. Expectedly, the social networks we study display power-law distributions; by Li’s measure, these net- works show scale-free properties as well.

Small-world networks have a small diameter and exhibit high clustering. Studies have shown that the Web [5,12], sci- entific collaboration on research papers [41], film actors [6], and general social networks [3] have small-world properties. Kleinberg [23] proposes a model to explain the small-world phenomenon in offline social networks, and also examines navigability in these networks [22]. The online social net- works examined in this paper have small-world properties much like their offline counterparts.

4. MEASUREMENT METHODOLOGY We now describe the data presented in this paper and the methodology we used to collect it. We were not able to ob- tain data directly from the respective site operators. Most sites are hesitant to provide even anonymized data, and sign- ing non-disclosure agreements to obtain data from multiple competing sites may not be feasible or desirable. Instead, we chose to crawl the user graphs by accessing the public web interface provided by the sites. This methodology gives us access to large data sets from multiple sites.

Since the focus of this paper is to investigate the struc- ture of online social networks, we focus on the large weakly connected component (WCC) of the corresponding graphs in the rest of this paper. As we show later in this section, the large WCC is structurally the most “interesting” part of the network. The nodes not included in the WCC tend to be either part of very small, isolated clusters or are not connected to other users at all.

4.1 Challenges in crawling large graphs Crawling large, complex graphs presents unique challenges. In this section, we describe our general approach before dis- cussing the details of how we crawled each network.

4.1.1 Crawling the entire connected component The primary challenge in crawling large graphs is covering the entire connected component. At each step, one can gen- erally only obtain the set of links into or out of a specified node. In the case of online social networks, crawling the graph efficiently is important since the graphs are large and highly dynamic. Common algorithms for crawling graphs include breadth-first search (BFS) and depth-first search.

Often, crawling an entire connected component is not fea- sible, and one must resort to using samples of the graph. Crawling only a subset of a graph by ending a BFS early (called the snowball method) is known to produce a biased sample of nodes [29]. In particular, partial BFS crawls are likely to overestimate node degree and underestimate the level of symmetry [10]. In social network graphs, collecting samples via the snowball method has been shown to un- derestimate the power-law coefficient, but to more closely match other metrics, including the overall clustering coeffi- cient [29].

Some previous studies of social networks have used small graph samples. Example studies have used samples of 0.3% of Orkut users [4], less than 1% of LiveJournal communi- ties [8], and 0.08% of MySpace users [4]. In this paper, we obtain and study much larger samples of the user graphs.

Flickr LiveJournal Orkut YouTube Number of users 1,846,198 5,284,457 3,072,441 1,157,827 Estimated fraction of user population crawled 26.9% 95.4% 11.3% unknown Dates of crawl Jan 9, 2007 Dec 9 - 11, 2006 Oct 3 - Nov 11, 2006 Jan 15, 2007 Number of friend links 22,613,981 77,402,652 223,534,301 4,945,382 Average number of friends per user 12.24 16.97 106.1 4.29 Fraction of links symmetric 62.0% 73.5% 100.0% 79.1% Number of user groups 103,648 7,489,073 8,730,859 30,087 Average number of groups memberships per user 4.62 21.25 106.44 0.25

Table 1: High-level statistics of our social networking site crawls.

4.1.2 Using only forward links Crawling directed graphs, as opposed to undirected graphs, presents additional challenges. In particular, many graphs can only be crawled by following links in the forward direc- tion (i.e., one cannot easily determine the set of nodes which point into a given node). Using only forward links does not necessarily crawl an entire WCC; instead, it explores the connected component reachable from the set of seed users. This limitation is typical for studies that crawl online net- works, including measurement studies of the Web [12].

START

ONLY USING

FORWARD LINKS

USING

BOTH FORWARD

AND REVERSE LINKS

Figure 1: Users reached by crawling different link types. If only forward links are used, we can reach only the inner cloud (shaded cloud); using both forward and reverse links crawls the entire WCC (dashed cloud).

Figure 1 shows an example of a directed graph crawl. The users reached by following only forward links are shown in the shaded cloud, and those reached using both forward and reverse links are shown in the dashed cloud. Using both for- ward and reverse links allows us to crawl the entire WCC, while using only forward links results in a subset of the WCC.

4.2 Crawling social networks We now discuss our methodology for crawling each of the networks we crawled, its limitations, and high-level statistics of the resulting data sets. Using automated scripts on a clus- ter of 58 machines, we crawled the social network graphs of Flickr, LiveJournal, Orkut, and YouTube. High-level statis- tics of the resulting data sets are presented in Table 1.

We chose these four sites because they are among the most popular social networking sites and they allow us to view the links out of any user in the network. In each step of our crawls, we retrieved the list of friends for a user we had not yet visited and added the retrieved users to the list of users to visit. We continued until we exhausted the list. This corresponds to a BFS of the social network graphs.

4.2.1 Flickr Flickr (www.flickr.com) is a photo-sharing site based on a social network. The Flickr data presented in this paper is from a crawl of the large WCC conducted on January 9th, 2007, and contains over 1.8 million users and 22 million links. Flickr exports an API for third-party developers, and we used this API to conduct the crawl. We also obtained group membership information via Flickr’s API.5

Flickr only allows us to query for forward links. Therefore we were unable to crawl the entire large WCC. To estimate the fraction of users who are part of the WCC but missing in our crawl, we performed the following experiment. We used the fact that the vast majority of Flickr user identifiers take the form of [randomly selected 8 digit number]@N00. We generated 100,000 random user identifiers of this form (from a possible pool of 90 million) and found that 6,902 (6.90%) of these were assigned usernames. These 6,902 nodes form a random sample of Flickr users.

Among these 6,902 users, 1,859 users (26.9%) had been discovered during our crawl. Focusing on the 5,043 users not previously discovered by our crawl, we conducted a BFS starting at each user to determine whether or not they could reach our set of previously crawled users. We found that only 250 (5.0%) of the missed users could reach our crawled set and were definitively in the WCC. While we cannot conclu- sively say that the remaining 4,793 (95.0%) missed users are not attached to the WCC (there could be some other user who points to them and to the WCC), the fact that 89.7% of these have no forward links suggests that many are not connected at all.

Finally, to explore how the remaining missing nodes are connected, we crawled the social network using these missing users as seeds, and compared the results with our initial crawl. We found only 11,468 new nodes that were not in the connected component of 1.8 million nodes discovered in the original crawl. Of these new nodes, 5,142 (44.8%) were singleton nodes with no forward links, 3,370 (29.3%) had one link, 620 (5.4%) had two or three links, and 2,336 (20.3%) had four or more links. Thus, the nodes missing from our crawls tend to have low degree and are connected only to small clusters that are not reachable from the large connected component we crawled.

Thus, we believe that our crawl of the large WCC, al- though not complete, covers a large fraction of the users who are part of the WCC. Further, our experience with the randomly generated Flickr user identifiers indicates that (at least for Flickr), the nodes not in the largest WCC do not form large subgraphs.

5Flickr allows users to form private groups, which do not appear in the user’s profile list. We were unable to determine any information about the membership of such groups.

4.2.2 LiveJournal LiveJournal (www.livejournal.com) is a popular blogging site whose users form a social network. The LiveJournal data set considered in this paper is the largest we examine: it contains over 5.2 million users and 72 million links. Due to its size, the LiveJournal crawl took several days, from December 9-11, 2006. LiveJournal offers an API that al- lows us to query for both forward and reverse links. We followed both link types to crawl the entire large WCC. We also obtained group membership information via LiveJour- nal’s API.6

To estimate the fraction of the LiveJournal network cov- ered by our crawl, we used a feature of LiveJournal7 that returns random users to select a list of 5,000 random Live- Journal users. We then checked how many of these random users our crawl had already covered. We found that we had already crawled 4,773 (95.4%) of these users, showing that our LiveJournal crawl covers the vast majority of the Live- Journal population. Finally, we started another crawl from the previously unknown 227 users to determine how many additional users could be discovered. This technique found only 73 additional users. These results suggest that our LiveJournal crawl covers almost the entire LiveJournal user population, and that the users not included in our crawl are part of small, isolated clusters.

Using the entire WCC from LiveJournal, we calculated the fraction of the WCC that is not reachable by using only forward links (as we did for the Flickr and YouTube crawls). We found that of the 5,284,457 nodes in the dis- covered weakly connected component, only 404,134 (7.64%) would have been missed had we followed only forward links. Finally, we examined the 404,134 users who would have been missed to see how well these users were connected. We found that 201,694 (49.9%) of these users had a single forward link, 86,561 (21.1%) had two or three links, and 78,463 (19.4%) of the users had four or more forward links. Since, as we will show later, Flickr and YouTube share many characteristics with LiveJournal, this result suggests that the users that are missing in our Flickr and YouTube crawls tend to be small in number and have relatively small outdegree.

4.2.3 Orkut The next site we examined is Orkut (www.orkut.com), a so- cial networking site run by Google. Orkut is a “pure” social network, as the sole purpose of the site is social networking, and no content is being shared. In Orkut, links are undi- rected and link creation requires consent from the target. Since, at the time of the crawl, new users had to be invited by an existing user to join the system, the Orkut graph forms a single SCC by definition.

The Orkut data considered in the paper was collected dur- ing a crawl performed between October 3rd and November 11th, 2006. Because Orkut does not export an API, we had to resort to HTML screen-scraping to conduct our crawl, which requires more bandwidth. We obtained group infor- mation in a similar manner. Furthermore, Orkut limits the rate at which a single IP address can download information and requires a logged-in account to browse the network. As a result, it took more than a month to crawl a subset of

6We inferred groups in LiveJournal by crawling the interests specified by users. 7 http://www.livejournal.com/random.bml

3,072,441 users, at which point we stopped. This subset cor- responds to 11.3% of Orkut’s user population of about 27 million users at the time of the crawl. The Orkut data con- sidered in this paper, therefore, is limited to this connected component and disregards all links from this component to other, uncrawled users.

Because our Orkut data set contains only a sample of the entire Orkut network, there are two potential concerns with the representativeness of the data. The first question is how the 11.3% subset of the network we gathered would compare to a different 11.3% subset gathered in the same way. In other words, are the properties of our sample representative of other samples of similar size? The second question is how the properties of our sample compare to the properties of the network as a whole.

To explore the first of these concerns, we conducted five separate, small crawls of Orkut starting from random lo- cations. Our random starting locations were chosen using Maximum-Degree random sampling [7] configured with a path length of 100,000 hops. Each of the five crawls was configured to cover 80,000 nodes in the same manner as our single, large crawl. We then examined how similar the prop- erties of the resulting samples were to each other.

We found that the properties of the five smaller crawls were similar, even though these crawls covered only 0.26% of the network. For example, we found that the clustering coefficient of these crawls had an average of 0.284 with a standard deviation of 0.040. Similarly, we found that the scale-free metric had an average of 0.550 with a standard deviation of 0.083 (both of these metrics are discussed in more detail in the following section). Thus, we believe that the properties of our 11.3% sample of the network are likely to be similar to other crawls of similar size that are done in the same manner.

However, we caution the reader to be mindful of the sec- ond concern when extrapolating the results from our crawl to the entire Orkut network. Partial BFS crawls are known to over-sample high-degree nodes, and under-sample low- degree nodes [29]. This has been shown to overestimate the average node degree and to underestimate the level of sym- metry [10]. Thus, our results may not be representative of the Orkut network as a whole.

4.2.4 YouTube YouTube (www.youtube.com) is a popular video-sharing site that includes a social network. The YouTube data we present was obtained on January 15th, 2007 and consists of over 1.1 million users and 4.9 million links. Similar to Flickr, YouTube exports an API, and we used this feature to con- duct our crawls.

YouTube allows links to be queried only in the forward direction, similar to Flickr. Unfortunately, YouTube’s user identifiers do not follow a standard format,8 and we were therefore unable to create a random sample of YouTube users. Also, YouTube does not export group information via the API. Instead, we obtained group membership infor- mation by screen-scraping the HTML pages attached to user profiles.

Because we were unable to crawl reverse links or estimate the size of the user population in YouTube, we advise the reader to be cautious in extrapolating the YouTube results

8YouTube’s user identifiers are user-specified strings.

to the entire YouTube population, as we do not know the number of users who do not participate in the social network.

4.2.5 Summary Our results indicate that

• The Flickr and YouTube data sets may not contain some of the nodes in the large WCC, but this fraction is likely to be very small.

• The LiveJournal data set covers almost the complete population of LiveJournal, and contains the entire large WCC.

• The Orkut data set represents a modest portion of the network, and is subject to the sampling bias resulting from a partial BFS crawl.

Moreover, the results also indicate that the vast majority of missed nodes in Flickr, LiveJournal, and YouTube have low degree and are likely to be part of small, isolated clus- ters.

Based on the number of users published by the sites at the time of the crawl, we estimate the fraction of nodes our crawls cover as 1.8 million out of 6.8 million (26.9%) for Flickr, 5.2 million of 5.5 million (95.4%) for LiveJour- nal, and 3.0 million out of 27 million (11.3%) for Orkut. Unfortunately, we do not know the number of accounts in YouTube. Thus, we were unable to estimate the fraction of the population that our 1.1 million crawled YouTube users represent.

All of the data sets considered in this paper are available to the research community. The data has been anonymized in order to ensure the privacy of the social network users. A detailed description of the data format and downloading instructions are available at http://socialnetworks.mpi-sws.mpg.de

4.3 High-level statistics Table 1 presents the high-level statistics of the data we gath- ered. The crawled network sizes vary by almost a factor of five (1.1 million users in YouTube vs. 5.2 million in Live- Journal), and the number of links varies by almost two or- ders of magnitude (4.9 million in YouTube versus 223 mil- lion in Orkut). Similarly, other metrics such as the average number of friend links per node and user participation in shared interest groups also vary by two to three orders of magnitude. Our analysis later will show that despite these differences, these graphs share a surprisingly large number of key structural properties.

4.4 Web graph analysis The Web is one of the most well-studied online networks, and our study shares much of its methodology with previ- ous studies of the Web. It is natural to compare the struc- ture of online social networks to the structure of the Web. However, we are well aware that the user graph in social net- works is fundamentally different from the Web graph; our comparisons serve more to provide a point of reference for our results than to point out (expected) differences.

In order to compare the structure of online social net- works with that of the Web, we cite previous studies of the Web structure where possible. We also performed some of our own analysis, using the data collected by the Stanford WebBase Project [1] during their crawl of December 2003.

We selected 8.6 million pages and 132 million hyperlinks collected from over 3,900 Web sites contained in the crawl.

5. ANALYSIS OF NETWORK STRUCTURE In this section, we characterize the structural properties of the four networks we measured. We compare the networks to each other, and we compare their properties with those previously observed for the Web.

5.1 Link symmetry The fact that links are directed can be useful for locat- ing content in information networks. For example, in the Web graph, search algorithms such as PageRank [43] con- sider a directed link from a source to a destination as an endorsement of the destination by the source, but not vice- versa. For instance, numerous Web pages point to sites like cnn.com or nytimes.com, but very few pages receive pointers back from these sites. Search engines leverage this to iden- tify reputed sources of information, since pages with high indegree tend to be authorities [21].

With the exception of Orkut, links in the social networks we studied are directed and users may therefore link to any other user they wish. The target of the link may reciprocate by placing a link pointing back at the source. Our anal- ysis of the level of symmetry in social networks, shown in Table 1, reveals that all three social networks with directed links (Flickr, LiveJournal, and YouTube) have a significant degree of symmetry. Their high level of symmetry is consis- tent with that of offline social networks [20]. Furthermore, social networking sites inform users of new incoming links, which may also contribute to the high level of symmetry.

Independent of the causes, the symmetric nature of social links affects the network structure. For example, symmetry increases the overall connectivity of the network and reduces its diameter. Symmetry can also make it harder to identify reputable sources of information just by analyzing the net- work structure, because reputed sources tend to dilute their importance when pointing back to arbitrary users who link to them.

5.2 Power-law node degrees We begin to examine the graph structure by considering the node degree distribution. As discussed in Section 3, the de- gree distributions of many complex networks, including of- fline social networks, have been shown to conform to power- laws. Thus, it may not be surprising that social networks also exhibit power-law degree distributions. However, as our analysis shows, the degree distributions in social networks differ from that of other power-law networks in several ways.

Figure 2 shows the outdegree and indegree complementary cumulative distribution function (CCDF) for each measured social network. All of the networks show behavior consistent with a power-law network; the majority of the nodes have small degree, and a few nodes have significantly higher de- gree. To test how well the degree distributions are modeled by a power-law, we calculated the best power-law fit using the maximum likelihood method [13]. Table 2 shows the estimated power-law coefficient along with the Kolmogorov- Smirnov goodness-of-fit metric [13]. While the best power- law coefficients approximate the distributions very well for Flickr, LiveJournal, and YouTube, the Orkut data deviates significantly.

Two factors contribute to this deviation. First, our Orkut

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Figure 2: Log-log plot of outdegree (top) and indegree (bottom) complementary cumulative distribution functions (CCDF). All social networks show properties consistent with power-law networks.

Outdegree Indegree Network α D α D Web [12] 2.67 - 2.09 - Flickr 1.74 0.0575 1.78 0.0278 LiveJournal 1.59 0.0783 1.65 0.1037 Orkut 1.50 0.6319 1.50 0.6203 YouTube 1.63 0.1314 1.99 0.0094

Table 2: Power-law coefficient estimates (α) and corresponding Kolmogorov-Smirnov goodness-of-fit metrics (D). The Flickr, LiveJournal, and YouTube networks are well approximated by a power-law.

crawl reached only 11.3% of the network — partial BFS crawls tend to undersample nodes with lower degree, which can explain the flat head of the distribution [29]. Second, both LiveJournal and Orkut artificially cap a user’s num- ber of outgoing links,9 which leads to a distortion in the distribution for high degrees.

Additionally, we tested the stability of the power-law co- efficient estimates by running the maximum likelihood esti- mator over varyingly sized subsamples of our data [53]. We found that the estimates of the power-law coefficient were remarkably stable; the estimates varied by less than 6% from those provided in Table 2 when we considered as few as 1,000 data points.

Table 2 also shows a difference between the structure of social networks and that of previously observed networks. In the Web, for example, the indegree and outdegree power- law exponents have been shown to differ significantly, while the power-law exponents for the indegree and outdegree dis- tributions in each of our social networks are very similar. This implies that in online social networks, the distribution of outgoing links is similar to that of incoming links, while in the Web, the incoming links are significantly more concen- trated on a few high-degree nodes than the outgoing links.

Focusing on this difference, Figure 3 shows the distribu- tion of incoming and outgoing links over nodes in the Web

9Orkut caps the outdegree at 1,000, and LiveJournal at 750. Both of these caps were instituted after the networks were established, and some users therefore exceed the caps. Also, Flickr has since instituted a cap of 3,000 non-reciprocal links; however, the data shown here was collected before this cap was established.

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Figure 3: Plot of the distribution of links across nodes. Social networks show similar distributions for outgoing and incoming links, whereas the Web links shows different distributions.

and Flickr graphs.10 The difference is readily apparent: 5% of the Web nodes account for 75% of all incoming links, but for only 25% of all outgoing links. In all social networks we considered, the distributions of incoming and outgoing links across the nodes are very similar. We now examine this phenomenon in more detail.

5.3 Correlation of indegree and outdegree Studies of the indegree and outdegree distributions in the Web graph helped researchers find better ways to find rel- evant information in the Web. In the Web, the population of pages that are active (i.e., have high outdegree) is not the same as the population of pages that are popular (i.e., have high indegree) [21]. For example, many Web pages of individual users actively point to a few popular pages like wikipedia.org or cnn.com. Web search techniques are very effective at separating a very small set of popular pages from a much larger set of active pages.

In social networks, the nodes with very high outdegree also tend to have very high indegree. In our study, for each network, the top 1% of nodes ranked by indegree has a more than 65% overlap with the top 1% of nodes ranked by out- degree. The corresponding overlap in the Web is less than 20%. Hence, active users (i.e., those who create many links)

10The Flickr topology is representative of all four networks; we omitted the others in the plot for readability.

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Figure 4: Plot of the overlap between top x% of nodes ranked by outdegree and indegree. The high- indegree and high-outdegree nodes are often the same in social networks, but not in the Web.

in social networks also tend to be popular (i.e., they are the target of many links). Figure 4 shows the extent of the overlap between the top x% of nodes ranked by indegree and outdegree.

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Figure 5: CDF of outdegree to indegree ratio. Social networks show much stronger correlation between indegree and outdegree than the Web.

Next, we compared the indegree and outdegree of individ- ual nodes in the social networks. Figure 5 plots the cumula- tive distributions of the outdegree-to-indegree ratio for the four social networks and the Web. The social networks show a remarkable correspondence between indegree and outde- gree; for all networks, over 50% of nodes have an indegree within 20% of their outdegree. The distribution for the Web is markedly different; most nodes have considerably higher outdegree than indegree, while a small fraction of nodes have significantly higher indegree than outdegree.

The high correlation between indegree and outdegree in social networks can be explained by the high number of symmetric links. The high symmetry may be due to the tendency of users to reciprocate links from other users who point to them. This process would result in active users (who place many outgoing links) automatically receiving many in- coming links, and lead to the distributions we have observed.

5.4 Path lengths and diameter Next, we look at the properties of shortest paths between users. Table 3 shows the average path lengths, diameters, and radii11 for the four social networks. In absolute terms, the path lengths and diameters for all four social networks

11The eccentricity of a node v is the maximal shortest path distance between v and any other node. The radius of a

Network Avg. Path Len. Radius Diameter Web [12] 16.12 475 905 Flickr 5.67 13 27 LiveJournal 5.88 12 20 Orkut 4.25 6 9 YouTube 5.10 13 21

Table 3: Average path length, radius, and diameter of the studied networks. The path length between random nodes is very short in social networks.

are remarkably short. Interestingly, despite being compara- ble in size to the Web graph we considered, the social net- works have significantly shorter average path lengths and diameters. This property may again result from the high degree of reciprocity within the social networks. Inciden- tally, Broder et al. [12] noted that if the Web were treated as an undirected graph, the average path length would drop from 16.12 to 7.

5.5 Link degree correlations To further explore the difference in network structure be- tween online social networks and previously observed net- works, we examine which users tend to connect to each other. In particular, we focus on the joint degree distribu- tion (JDD), or how often nodes of different degrees connect to each other. This property is also referred to as the 2K- distribution [33] or the mixing patterns [42].

5.5.1 Joint degree distribution The JDD provides many insights into the structural proper- ties of networks. For example, networks where high-degree nodes tend to connect to other high-degree nodes are more likely to be subject to epidemics, as a single infected high- degree node will quickly infect other high-degree nodes. On the other hand, networks where high-degree nodes tend to connect to low-degree nodes show the opposite behavior; a single infected high-degree node will not spread an epidemic very far.

The JDD is approximated by the degree correlation func- tion knn, which is a mapping between outdegree and the average indegree of all nodes connected to nodes of that out- degree. Clearly, an increasing knn indicates a tendency of higher-degree nodes to connect to other high-degree nodes; a decreasing knn represents the opposite trend. Figure 6 shows a plot of knn for the four networks we studied.

The trend for high-degree nodes to connect to other high- degree nodes can be observed in all networks except YouTube (the unexpected bump at the head of the Orkut curve is likely due to the undersampling of users). This suggests that the high-degree nodes in social networks tend to connect to other high-degree nodes, forming a “core” of the network. Anecdotally, we believe that the different behavior seen in YouTube is due its more “celebrity”-driven nature; there are a few extremely popular users on YouTube to whom many unpopular users connect.

graph is then the minimum eccentricity across all vertices, and the diameter is the maximum eccentricity across all vertices. Due to the computational complexity associated with determining the actual radius and diameter, the num- bers presented here are from determining the eccentricity of 10,000 random nodes in each network. Therefore, the diam- eter should be viewed as a lower bound, and the radius as an upper bound.

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Figure 6: Log-log plot of the outdegree versus the average indegree of friends. The scale-free metrics, included in the legend, suggest the presence of a well-connected core.

To quantitatively explore this phenomenon, we next ex- amine two metrics based on the joint degree distribution: the scale-free metric s and the assortativity r.

5.5.2 Scale-free behavior The scale-free metric s [31] is a value calculated directly from the joint degree distribution of a graph. The scale-free metric ranges between 0 and 1, and measures the extent to which the graph has a hub-like core. A high scale-free metric means that high-degree nodes tend to connect to other high- degree nodes, while a low scale-free metric means that high- degree nodes tend to connect to low-degree nodes.

The scale-free metric of the networks are shown in the legend of Figure 6. All of the networks with the exception of YouTube show a significant s, indicating that high-degree nodes tend to connect to other high-degree nodes, and low- degree nodes tend to connect to low-degree nodes.

5.5.3 Assortativity The scale-free metric is related to the assortativity coeffi- cient r, which is a measure of the likelihood for nodes to con- nect to other nodes with similar degrees. The assortativity coefficient ranges between -1 and 1; a high assortativity coef- ficient means that nodes tend to connect to nodes of similar degree, while a negative coefficient means that nodes likely connect to nodes with very different degree from their own Recent work has suggested that the scale-free metric is more suitable for comparing the structure of different graphs [30], as it takes into account the possible configurations of net- works with properties including connectedness and no self- loops. However, for completeness, we calculated the assorta- tivity coefficients for each of the networks, and found 0.202 for Flickr, 0.179 for LiveJournal, 0.072 for Orkut, and -0.033 for YouTube.

The assortativity shows yet another difference between the social networks and other previously observed power- law networks. For example, the Web and the Internet have both been shown to have negative assortativity coefficients of -0.067 and -0.189, respectively [42]. On the other hand, many scientific coauthorship networks, a different type of social network, have been shown to have positive r [42].

Taken together, the significant scale-free metric and the positive assortativity coefficient suggests that there exists a tightly-connected “core” of the high-degree nodes which connect to each other, with the lower-degree nodes on the fringes of the network. In the next few sections, we explore the properties of these two components of the graph in de- tail.

5.6 Densely connected core We loosely define a core of a network as any (minimal) set of nodes that satisfies two properties: First, the core must be necessary for the connectivity of the network (i.e., removing the core breaks the remainder of the nodes into many small, disconnected clusters). Second, the core must be strongly connected with a relatively small diameter. Thus, a “core” is a small group of well-connected group of nodes that is necessary to keep the remainder of the network connected.

To more closely explore the core of the network, we use an approximation previously used in Web graph analysis [12]. Specifically, we remove increasing numbers of the highest degree nodes and analyze the connectivity of the remaining graph.12 We calculate the size of the largest remaining SCC, which is the largest set of users who can mutually reach each other.

As we remove the highest degree nodes, the largest SCC begins to split into smaller-sized SCCs. Figure 7 shows the composition of the splits as we remove between 0.01% and 10% of the highest-degree nodes in Flickr. The correspond- ing graphs for the other social networks look similar, and we omit them for lack of space. Once we remove 10% of the highest indegree nodes,13 the largest SCC partitions into millions of very small SCCs consisting of only a handful of nodes.

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Figure 7: Breakdown of network into SCCs when high-degree nodes are removed, grouped by SCC size.

To understand how much the network core contributes to- wards the small path lengths, we analyzed the path lengths

12The large size of the graphs we study makes a cut set anal- ysis computationally infeasible.

13We obtained the same results using both indegree and out- degree.

of subgraphs containing only the highest-degree nodes. Fig- ure 8 shows how path lengths increase as we generate larger subgraphs of the core by progressively including nodes or- dered inversely by their degree. The average path length increases sub-logarithmically with the size of the core. In Flickr, for example, the overall average path length is 5.67, of which 3.5 hops involve the 10% of nodes in the core with the highest degrees. This suggests that the high-degree core nodes in these networks are all within roughly four hops of each other, while the rest of the nodes, which constitute the majority of the network, are at most a few hops away from the core nodes.

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Figure 8: Average path length among the most well- connected nodes. The path length increases sub- logarithmically.

Thus, the graphs we study have a densely connected core comprising of between 1% and 10% of the highest degree nodes, such that removing this core completely disconnects the graph.

The structure of social networks, with its high dependence on few highly connected nodes, may have implications for information flow, for trust relationships, and for the vulner- ability of these networks to deliberate manipulation. The small diameter and path lengths of social networks are likely to impact the design of techniques for finding paths in such networks, for instance, to check how closely related a given pair of nodes is in the network. Such techniques have ap- plications, for instance, in social networks used to verify the trustworthiness or relevance of received information [17].

5.7 Tightly clustered fringe Next, we consider the graph properties at the scale of local neighborhoods outside of the core. We first examine clus- tering, which quantifies how densely the neighborhood of a node is connected.

The clustering coefficient of a node with N neighbors is defined as the number of directed links that exist between the node’s N neighbors, divided by the number of possible directed links that could exist between the node’s neighbors (N (N − 1)). The clustering coefficient of a graph is the average clustering coefficient of all its nodes, and we denote it as C.

Table 4 shows the clustering coefficients for all four social networks. For comparison, we show the ratio of the observed clustering coefficient to that of Erdös-Réyni (ER) random graphs [15] and random power-law graphs constructed with preferential attachment [9], with the same number of nodes and links. ER graphs have no link bias towards local nodes. Hence, they provide a point of reference for the degree of local clustering in the social networks. Graphs constructed

Ratio to Random Graphs Network C Erdös-Rényi Power-Law Web [2] 0.081 7.71 - Flickr 0.313 47,200 25.2 LiveJournal 0.330 119,000 17.8 Orkut 0.171 7,240 5.27 YouTube 0.136 36,900 69.4

Table 4: The observed clustering coefficient, and ra- tio to random Erdös-Réyni graphs as well as random power-law graphs.

using preferential attachment also have no locality bias, as preferential attachment is a global process, and they provide a point of reference to the clustering in a graph with a similar degree distribution.

The clustering coefficients of social networks are between three and five orders of magnitude larger than their corre- sponding random graphs, and about one order of magnitude larger than random power-law graphs. This unusually high clustering coefficient suggests the presence of strong local clustering, and has a natural explanation in social networks: people tend to be introduced to other people via mutual friends, increasing the probability that two friends of a sin- gle user are also friends.

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Figure 9 shows how the clustering coefficients of nodes vary with node outdegree. The clustering coefficient is higher for nodes of low degree, suggesting that there is significant clustering among low-degree nodes. This clustering and the small diameter of these networks qualifies these graphs as small-world networks [52], and further indicates that the graph has scale-free properties.

5.8 Groups In many online social networks, users with shared interests may create and join groups. Table 5 shows the high-level statistics of user groups in the four networks we study. Par- ticipation in user groups varies significantly across the differ- ent networks: only 8% of YouTube users but 61% of Live- Journal users declare group affiliations. Once again, the group sizes follow a power-law distribution, in which the vast majority have only a few users each.

Note that users in a group need not necessarily link to each other in the social network graph. As it turns out, however, user groups represent tightly clustered communi- ties of users in the social network. This can be seen from the average group clustering coefficients of group members,

Network Groups Usage Avg. Size Avg. C Flickr 103,648 21% 82 0.47 LiveJournal 7,489,073 61% 15 0.81 Orkut 8,730,859 13% 37 0.52 YouTube 30,087 8% 10 0.34

Table 5: Table of the high-level properties of net- work groups including the fraction of users which use group features, average group size, and average group clustering coefficient.

shown in Table 5.14 These coefficients are higher than those of the corresponding network graph as a whole (shown in Table 4). Further, the members of smaller user groups tend to be more clustered than those of larger groups. Figure 10 shows this by plotting the average group clustering coeffi- cient for groups of different sizes in the four observed net- works. In fact, many of the small groups in these networks are cliques.

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Figure 10: Plot of group size and average group clus- tering coefficient. Many small groups are almost cliques.

Finally, Figure 11 shows how user participation in groups varies with outdegree. Low-degree nodes tend to be part of very few communities, while high-degree nodes tend to be members of multiple groups. This implies a correlation be- tween the link creation activity and the group participation. There is a sharp decline in group participation for Orkut users with over 500 links, which is inconsistent with the be- havior of the other networks. This result may be an artifact of our partial crawl of the Orkut network and the resulting biased user sample.

In general, our observations suggest a global social net- work structure that is comprised of a large number of small, tightly clustered local user communities held together by nodes of high degree. This structure is likely to significantly impact techniques, algorithms and applications of social net- works.

5.9 Summary We end this section with a brief summary of important struc- tural properties of social networks which we observed in our data.

• The degree distributions in social networks follow a power-law, and the power-law coefficients for both in-

14We define the group clustering coefficient of a group G as the clustering coefficient of the subgraph of the network con- sisting of only the users who are members of G.

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degree and outdegree are similar. Nodes with high indegree also tend to have high outdegree.

• Social networks appear to be composed of a large num- ber of highly connected clusters consisting of relatively low-degree nodes. These clusters connect to each other via a relatively small number of high-degree nodes. As a consequence, the clustering coefficient is inversely proportional to node degree.

• The networks each contain a large, densely connected core. Overall, the network is held together by about 10% of the nodes with highest degree. As a result, path lengths are short, but almost all shortest paths of sufficient length traverse the highly connected core.

6. DISCUSSION In this section, we discuss some implications of our findings. Our measurements indicate that online social networks have a high degree of reciprocity, a tight core that consists of high- degree nodes, and a strong positive correlation in link de- grees for connected users. What do these findings mean for developers? Alternately, how should applications for social networks be designed to take advantage of these properties? Do these properties reveal straightforward attacks on the social structure? Finally, does it make sense to “optimize” algorithms and applications based upon our findings, since these networks are still growing rapidly and any property we assert now may soon change?

While our findings are likely applicable to many different applications, we concentrate on their effect on information dissemination, search, and trust inference.

6.1 Information dissemination and search Social networks are already used as a means for rapidly dis- seminating information, as witnessed by the popularity of “hot” videos on YouTube. The existence of a small, well- connected core implies that information seeded via a core node will rapidly spread through the entire network. This is both a strength and a weakness, as spam or viruses could be disseminated this way, as well as important information.

Similarly, searches that proceed along social network links will quickly reach the core. This suggests that simple un- structured search algorithms could be designed if the core users were to store some state about other users. In effect, the users in the core represent “supernodes” in a two-level hi- erarchy, similar to existing search protocols for unstructured networks, such as Gnutella.

6.2 Trust Social networking sites are the portals of entry into the In- ternet for many millions of users, and they are being used both for advertisement as well as for the ensuing commerce. Many of these applications, ranging from mail to auctions, implicitly rely on some form of trust. For example, when a user accepts email from an unknown user, she is trusting the other party not to send spam. When a user selects a winning bidder in an auction, she is trusting the other party to pay the winning amount, and the winning user is trusting the seller to produce the auctioned item.

In a social network, the underlying user graph can po- tentially be used as a means to infer some level of trust in an unknown user [28], to check the validity of a public key certificate [38], and to classify potential spam [17]. In all of these, trust is computed as a function of the path between the source and target user.

Our findings have interesting implications for trust infer- ence algorithms. The tight core coupled with link reciprocity implies that users in the core appear on a large number of short paths. Thus, if malicious users are able to pene- trate the core, they can skew many trust paths (or appear highly trustworthy to a large fraction of the network). How- ever, these two properties also lead to small path lengths and many disjoint paths, so the trust inference algorithms should be adjusted to account for this observation. In par- ticular, given our data, an unknown user should be highly trusted only if multiple short disjoint paths to the user can be discovered.

The correlation in link degrees implies that users in the fringe will not be highly trusted unless they form direct links to other users. The “social” aspect of these networks is self- reinforcing: in order to be trusted, one must make many “friends”, and create many links that will slowly pull the user into the core.

6.3 Temporal invariance One possible criticism of our study is the snapshot character of our data, which does not account for change over time. To explore this, we repeated the entire crawl for both Flickr and YouTube on May 7th, 2007, and recomputed the complete statistics on the new data set. Both of the networks showed rapid growth over this five month time period, with Flickr growing by 38% and YouTube by 83%.

However, the salient observations in our original data are still valid; for Flickr, most of the updated results are indis- tinguishable from the results presented. YouTube showed a difference due to a policy change between our original and new crawls: YouTube switched from directed links to a two- phase symmetric link creation process. Thus, in the new YouTube crawl, we observe a much higher level of symme- try and a correspondingly larger SCC. However, many of the other metrics, such as the assortativity, clustering coef- ficient, and average path length are similar.

This experiment gives us some assurance that our struc- tural observations are not incidental to the stage of growth at which we sampled the network. Our data indicates that, even though the networks are growing rapidly, their basic structure is not changing drastically.

7. CONCLUSIONS We have presented an analysis of the structural properties of online social networks using data sets collected from four

popular sites. Our data shows that social networks are struc- turally different from previously studied networks, in partic- ular the Web. Social networks have a much higher fraction of symmetric links and also exhibit much higher levels of lo- cal clustering. We have outlined how these properties may affect algorithms and applications designed for social net- works.

Much work still remains. We have focused exclusively on the user graph of social networking sites; many of these sites allow users to host content, which in turn can be linked to other users and content. Establishing the structure and dynamics of the content graph is an open problem, the so- lution to which will enable us to understand how content is introduced in these systems, how data gains popularity, how users interact with popular versus personal data, and so on.

Acknowledgments We thank the anonymous reviewers, our shepherd Yin Zhang, and Walter Willinger for their helpful comments. We would also like to thank Anja Feldmann and Nils Kammenhuber for their assistance with the TU Munich trace. This research was supported in part by US National Science Foundation grant ANI-0225660.

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