WEB 2.0 and Social Networks Essay - 6 Oct - APA - 6 pages - 4 reference - Plagiarism-Free

The structural evolution of the Web 2.0 service network

Junseok Hwang, Jörn Altmann and Kibae Kim Department of Industrial Engineering, Seoul National University, Seoul,

South Korea

Abstract

Purpose – The purpose of this research is to empirically analyse the structure of the Web 2.0 service network and the mechanism behind its evolution over time.

Design/methodology/approach – Based on the list of Web 2.0 services and their mashups that is provided on Programmableweb, a network of Web 2.0 services was constructed. Within this network a node represents a Web 2.0 service with an open API, and a link between two nodes represents the existence of a mashup service that uses the two nodes.

Findings – The findings suggest that the evolution of the Web 2.0 service network follows the preferential attachment rule although the exponent of the preferential attachment is lower than for other networks following a preferential attachment rule. Additionally the results indicate that the Web 2.0 service network evolves to a scale-free network but the exponent of the power law distribution is lower than for other networks.

Originality/value – The research applied social network analysis to the Web 2.0 service network. It showed that its network structure and the evolution mechanism are different from those found in similar areas, e.g. the world wide web (WWW). The findings imply that there are factors which lower the exponent of the preferential attachment equation and the power law distribution of the degree centralities.

Research limitation/implications – This paper did not investigate the factors responsible for the low values of the exponent of the preferential attachment equation and the exponent of the power law distribution. However, it is suggested that it could be correlated with the fact that the interconnection between nodes depends on the property of the nodes.

Keywords Worldwide web, Internet, Social networks, Computer communications software

Paper type Research paper

Introduction The progress of Really Simple Syndication (RSS) technology and the introduction of asynchronous JavaScript and XML (AJAX) have propelled the success of new types of services on the internet (e.g. blogs) (Lai and Turban, 2008; O’Reilly, 2007), facilitating user-created web content. This differs from the first generation web, which simply distributed static content from providers to users. The term Web 2.0, which refers to this new generation of web sites, was used for the first time in October 2004 (O’Reilly, 2007). Web 2.0 is defined as new internet services which enable “users to collaboratively create, share and recreate knowledge from multiple sources, leverage collective intelligence and organise action” (Eijkman, 2008, p. 94). For example,

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1468-4527.htm

This research was supported by the Korea Communications Commission, Korea, under the Communications Policy Research Centre support programme supervised by the Institute for Information Technology Advancement.

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Refereed article received 10 November 2008 Approved for publication 15 July 2009

Online Information Review Vol. 33 No. 6, 2009 pp. 1040-1057 q Emerald Group Publishing Limited 1468-4527 DOI 10.1108/14684520911010990

YouTube, which offers a platform for sharing video clips made by users, provides an Application Programming Interface (API) so that users can access video clips from other (end-user) websites. In general these APIs allow users to mash up (i.e. combine) one or more Web 2.0 services in order to create their own composite value-added services (Floyd et al., 2007; Weiss, 2005; Zammetti, 2007).

Floyd et al. (2007) argue that the success of Web 2.0 comes from the opportunity to share resources. This explains the fast growth of the Web 2.0 service network. However, the network structure of Web 2.0 services has not been explained in previous research. It is also not clear how this network evolves over time, although researchers have suggested that the characteristics of the Web 2.0 service network are the reason for the effortless interactions between Web 2.0 services (Lai and Turban, 2008). Thus it is necessary to understand the structure and the mechanism behind the evolution of the Web 2.0 service network. This research aims to analyse the network characteristics and the evolution mechanism of the Web 2.0 service network using social network analysis (SNA).

Some existing literature on social networks deals with self-organisation of networks. Researchers have suggested that simple rules describing the behaviour of individuals may lead to the emergence of a unique pattern for the whole system. Self-organised systems have been investigated in various areas (e.g. academic collaboration, society and the WWW). It has been found that these networks are scale-free, which means that the degree distribution follows a power law (Albert and Barabási, 2002; Huberman and Adamic, 1999). The power law is defined as a mathematical equation between two variables P and k, such that PðkÞ ¼ k2g where g is the exponent which represents the characteristic of the degree centrality distribution of the network.

One of the most famous simple rules leading to a scale-free network is the preferential attachment rule, which describes the linkage formation. It states that the more popular a node is, the greater the likelihood that a link will be attached to it (Barabási, 2003). Some theoretical research has proved that the preferential attachment rule with an exponent close to 1 makes a network become a scale-free network with an exponent between 2 and 3 (Krapivsky et al., 2000; Barabási et al., 2001; Hołyst et al., 2004; Dorogovtsev et al., 2000). Some empirical research has verified the existence of a preferential attachment rule and scale-free structure for journal citation networks and for the WWW hyperlink network (Albert and Barabási, 2002; Barabási et al., 2001; Jeong et al., n.d.; Kujawski et al., 2007; Newman, 2001). Fu et al. (2008) analysed the structure of blogs and social network sites. They found a scale-free network structure with an exponent between 2 and 3. However, the Web 2.0 service network structure has not yet been analysed.

For our analysis, we used empirical data on Web 2.0 services surveyed on the website www.programmableweb.com, which lists Web 2.0 services with open APIs and their mashups. The data was used to construct the Web 2.0 service network that we used for our study. The nodes of this network are Web 2.0 services with open APIs and a link (also called a tie or connection) between two nodes represents the existence of a mashup that is constructed of at least those Web 2.0 services. In order to check whether the Web 2.0 service network is a scale-free network and whether it follows the preferential attachment rule, we calculated the ratio of the degree of a node to the sum of the degree of all nodes in the network.

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The analysis showed that the Web 2.0 service network is a scale-free network, following the preferential attachment rule. However, the exponent of the power law distribution and the exponent of the preferential attachment rule are lower than those for other self-organising networks. This implies that certain characteristics of the Web 2.0 service network affect the evolution of the network, which could not be explained within the parameters of the preferential attachment rule. As we will discuss in more detail, it could be because the interconnection between nodes depends on the property of the node or the type of node.

Prior research Web 2.0 services A Web 2.0 service API defines the interface for accessing service functions or data. Some Web 2.0 service companies release APIs so that any user can integrate applications into their website and thereby create a new Web 2.0 service (Weiss, 2005). The Web 2.0 service providers have an incentive to provide APIs, since it allows them to gain revenue from mashups that are developed by other commercial Web 2.0 service developers. Revenue from mashups could come from advertising (Roush, 2005). A Web 2.0 mashup is defined as a Web 2.0 service composed of one or more Web 2.0 services (Floyd et al., 2007). The success of Web 2.0 mashups is due to the efficient division of labour between providers. Mashup developers create new Web 2.0 services by combining existing Web 2.0 services, adding value to them (Floyd et al., 2007; Zammetti, 2007).

Web 2.0 services with an open API can be represented as a network in which a node is a Web 2.0 service with an open API. A link between nodes exists if both services have been used together in a Web 2.0 mashup. We call this network a “Web 2.0 service network”. Figure 1 includes the example of a mashup called Actor Tracker. It combines the Web 2.0 services of eBay and Amazon eCommerce.

The Web 2.0 service network as a social network The Web 2.0 service network can be considered a representation of the collective intelligence of the developers of Web 2.0 services (O’Reilly, 2007). Collective

Figure 1. Web 2.0 service network consisting of Web 2.0 services connected by mashups

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intelligence is “empowerment through the development and pooling of intelligence to attain common goals or resolve common problems” (Brown and Lauder, 2000, p. 234). Additionally, Kapetanios (2008, p. 289) defined collective intelligence as “human-computer systems in which machines enable the collection and harvesting of a large amount of human-generated knowledge”. Ensuring a high level of collective intelligence, the Web 2.0 service network acts as the host and organiser of innovation resources. A user has an incentive to voluntarily participate in the innovation if it accurately fulfils their needs (von Hippel, 2001). The issue is how the cyber society can stimulate the innovation resources (e.g. the functions and data) that each user and developer possesses and contributes. The Web 2.0 service network accomplishes this by offering development and diffusion of Web 2.0 services at a low cost. This is consistent with von Hippel’s theory of development community. The community lowers the cost barriers so that users can achieve innovation easily.

Network analysis As interaction between entities became a significant factor of innovation, innovation studies began to use social network analysis to investigate the relationship between entities (Smart et al., 2007). In particular the structure, the position of nodes, and the evolution mechanism of the social network can be analysed. The two main disciplines using social network analysis (SNA) are sociology and physics. By abstracting the relationships of actors as links between nodes, SNA offers a methodology to understand the structural characteristics of social phenomena. This analysis is useful in various areas such as designing effective communication networks (Monsuur, 2007) and efficient peer-to-peer social networks (Wang and Sun, 2008).

Sociologists are interested in the position of agents in the network and the network structures. In order to measure these characteristics they developed network indices and coefficients such as centrality, cliques and distance (Brass, 1984; Wasserman and Faust, 1994). For example, Everard and Henry (2002) investigated the degree centrality (the number of neighbours) and the betweenness centrality (the number of paths through the node) of an interlocked directorate of e-commerce companies. They concluded that companies bridging e-commerce companies with established leading companies are the most successful. Rodan (2008) developed an agent-based model, which considers the degree and the “cross-cutting ties” of an agent. The findings suggested that the effect of the degree of a node and the cross-cutting ties between groups had a positive affect on their learning performance (Rodan, 2008). By measuring the degree centrality of keywords and authors in Wikipedia, Korfiatis et al. (2006) investigated the heterogeneity of co-editions and the contributions of a variety of authors.

While sociologists have been concerned with the roles of agents and their relationships with the network structure, physicists have analysed the internal structure of networks and their evolution mechanisms. They have shown statistically that many real networks are heterogeneous, unlike the homogenous model of Erdös and Réiny (Barabási and Albert, 1999; Watts and Strogatz, 1998). Watts and Strogatz (1998) called networks with few nodes and a significantly large number of links in a short path between any two nodes “small world networks”. Barabási and Albert (1999) found that the distribution of the degree of nodes follows a power law, and they called this kind of network “scale-free”. Its exponents are generally between 2 and 3.

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Scale-free networks possess characteristics such as robustness against failure of a node, fragility against intended attack, and the sand pile effect (Albert et al., 2000; Tu, 2000). By analysing co-developers and co-project relationships in the open source software community, Xu et al. (2006) showed that the network of open source software is scale-free. In their analysis, the exponent of the power law of the developers’ network is about 3.3, which is quite high. Moreover, Angus et al. (2008) showed that the distribution of tagged images in Flickr is scale-free, which implies tags are used in a social and cultural context.

Evolution of networks Many researchers have suggested that a preferential attachment rule guides the construction of scale-free networks (Barabási and Albert, 1999; Dorogovtsev et al., 2000; Holyst et al., 2004; Krapivsky et al., 2000; Kujawski et al., 2007; Newman, 2001; Park et al., 2005; Štefančić and Zlatić, 2005). Barabási and Albert (1999) developed a model in which the probability that a new node links to existing nodes relates to the degrees of the existing nodes. Newman (2001) suggested a model in which the probability that two nodes are linked depends on the number of common acquaintances of each node. Through the growing random graph model, Krapivsky et al. (2000) determined that the linear probability of new attachments to existing nodes leads to a power-law distribution with an exponent between 2 and infinity. Barabási et al. (2001) applied a continuum equation that included the effect of newcomers and internal links. They concluded that scale-free networks should have an exponent between 2 and 3. Using supremacy, which means the number of nodes included in the subgraph from a certain node, Hołyst et al. (2004) derived a scale-free network from the preferential attachment rule. Dorogovtsev et al. (2000) mathematically derived a power law distribution of degree with exponents between 2 and 3 from the preferential attachment rule whose attractiveness is linear with degree.

Two approaches support these analyses. First, from a variety of fields the empirical data about networks provide evidence that the preferential attachment rule self-organises scale-free networks. A citation network, an actor network and the internet have been investigated (Albert and Barabási, 2002; Barabási et al., 2001; Jeong et al., n.d.; Kujawski et al., 2007; Newman, 2001). The three networks show a linear probability for new attachments to existing nodes and a power law distribution with exponents between 2 and 3 (Albert and Barabási, 2002; Barabási et al., 2001; Jeong et al., n.d.). Focusing on threads of postings, Kujawski et al. (2007) measured the topological and temporal statistics of internet discussions, which grow like a tree network. Newman (2001) investigated the citation network of databases in physics, biology and medicine. He found that the existence of common acquaintances affects the probability of new links. Valverde and Solé (2007) surveyed data from an open source project (SourceForge) to analyse the structure of the open source community. They found that open source social networks were self-organised into a scale-free network with an exponent of 2, and that it has a hierarchical design. Using blog service (Sina blog) data and social network site (Xiaonei SNS) data, Fu et al. (2008) analysed the structure of their social networks. Their results showed that both the Sina network and the Xiaonei network are scale-free. The exponent of the former is 2.34 and that of the latter is 2.12 (Fu et al., 2008).

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Second, to connect the established analytical models and empirical findings, the simulation approach evaluates the effect of the preferential attachment rule on the evolution of scale-free networks. Davidsen et al. (2002) tried to couple small world and scale-free networks by modelling an acquaintance network, in which nodes were linked to each other through a common acquaintance. Park et al. (2005) modelled a re-wiring link model to determine if non-growing networks can also be self-organising and scale-free. Štefančić and Zlatić (2005) established a two-step model (setting a group randomly and choosing a group preferentially) and explained that incomplete information can affect the evolution of networks. Schnegg and Stauffer (2007) unified the Erdös-Rényi model and the Barabási-Albert model to explain empirical analyses of the social networks of kinship and business in local societies. Some of the networks were similar to the scale-free network, but others’ distribution of degree looked like a reversed U-curve. The simulation of the Schnegg and Stauffer (2007) model indicated that the larger the effect of the preferential attachment, the larger the exponent of the power law distribution.

Research model Definitions To describe the preferential attachment rule and the scale-free property of the Web 2.0 service network, we first define the Web 2.0 service network. A Web 2.0 service with an open API is represented by a node. A Web 2.0 mashup created through a combination of Web 2.0 services is expressed as a link between nodes. For example, the mashup FeedFlinger is created by four Web 2.0 services (Yahoo! Terms, Yahoo! Search, Feed Burner and delicious.com), generating six links in the Web 2.0 service network. We assume that all nodes already exist and a multitude of links appear continuously between the nodes. Though nodes are created, updated and die in the real network, our assumption is based on the lack of data about updates and deaths in Web 2.0 services.

Degree centrality, which defines the number of links of a node, is a basic indicator in this research. It indicates the position of a node in a network. A high degree centrality means high accessibility to other nodes (Wasserman and Faust, 1994). Links are treated as undirected links because a link between Web 2.0 services to create a mashup does not distinguish a starting point and an end point of the link. The precise definition is as follows:

Definition 1. Degree centrality of node i at period t is the number of undirected links of node i.

For our analysis, degree centrality was normalised with respect to all links (called shareness) in the network for two reasons. First, the probability of linking to a node depends on the proportion of the degree centrality of a node to all degree centralities in the network. Second, the ratio is appropriate for comparing the degree centralities of nodes of different networks. This is essential since the number of links generated in each period is not uniform.

Definition 2. Shareness is the ratio of the number of links of a node to the total number of links in the network.

To be able to observe change over time, the definition of shareness was modified into two types: instant shareness and accumulated shareness. The former was designed to

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measure the ratio of new links of a node to those of all nodes in a period. The latter was devised to express the preference of new links to a node. Their definitions are as follows:

Definition 3. The instant shareness of node i at period t is the ratio of degree centrality of node i to the sum of degree centrality of all the nodes in the network at period t.

riðtÞ ¼ ciðtÞP j[IcjðtÞ

ð1Þ

Definition 4. The accumulated shareness of node i at period T is the ratio of the sum of the degree centrality of node i over all time periods to the sum of degree centrality of all the nodes in the network over all time periods.

RiðTÞ ¼

PT t¼0ciðtÞ

P j[I

PT t¼0cjðtÞ

ð2Þ

Here, I is a set of all the nodes in the network.

Preferential attachment The preferential attachment rule that we use is: a node with high degree centrality has a higher probability of obtaining new links than a node with low degree centrality. Thus a linkage to a node with high accessibility to the network provides more benefits than one with low accessibility. Users who create Web 2.0 mashups may choose Web 2.0 services with high degree centrality. Web 2.0 services with high degree centrality have high visibility in the Web 2.0 service network. For example, Programmableweb (www.programmableweb.com) provides a variety of rankings and tags of Web 2.0 services and mashups. Indirectly, users searching for appropriate Web 2.0 services for their mashups can reach the Web 2.0 services with high degree centrality through their neighbours more easily than they can reach those with low centrality.

The classic preferential attachment rule considers the attachment probability of a node as a function of the ratio of existing linkages of the node (Barabási et al., 2001; Krapivsky et al., 2000). The model is based on the assumption that the probability of new attachments is a power function of existing degree centrality. Prior research investigated whether the exponent of the power function is larger than 1, lower than 1 or linear. In our research accumulated and instant shareness are designed to measure existing proportional linkage and to calculate new attachment probability. Following the Barabási and Albert (1999) model, we formulated the hypothesis that instant shareness may depend on accumulated shareness by a power function (equation 3).

H1. The instant shareness of Web 2.0 service i at period t is linearly proportional to the accumulated shareness of Web 2.0 service i until period t-1.

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riðtÞ , Riðt 2 1Þ a ð3Þ

A factor affecting the preference of a node can be expanded from the relation between nodes to the attribute of the node. One assumes that users choose Web 2.0 services with high performance, which is suggested by the competency of the companies providing them. For example, if a large company such as Yahoo is interested in a Web 2.0 service and invests in it, then the preference of the Web 2.0 service may increase due to the high confidence placed in it. In this research we assumed that networks managed by Web 2.0 service providers such as Yahoo Developer Network may have a competitive advantage in attracting users who want to create new mashups. The Web 2.0 service attribute was modelled through a dummy variable, Di, which is 1 if the Web 2.0 service is provided by a company i operating its own network of developers; otherwise it is 0. The dummy variable for a developer’s web was assumed to have a linear relationship with instant shareness. This is expressed in the following hypothesis:

H2. The instant shareness of Web 2.0 service i at period t depends on the dummy variable of the developer’s web.

riðtÞ , bDi ð4Þ

Scale-free network Degree centrality indicates the position of Web 2.0 services within the network. As found by many previous researchers the degree centrality distribution of self-organised networks shows the power law distribution (Albert and Barabási, 2002; Barabási et al., 2001; Jeong et al., n.d.; Kujawski et al., 2007; Newman, 2001). Self-organised networks are likely to evolve toward the state where few nodes become hubs and the majority of nodes take few links. The Web 2.0 service network may show power law distribution because it is also self-organised via users’ selections for creating Web 2.0 mashups. The last hypothesis states that the structure of a Web 2.0 service network evolves into a scale-free network. This hypothesis is denoted by equation (5) where k is the accumulated degree centrality until period t, P(k, t) is the degree distribution at period t, and g is the exponent that represents the heterogeneity of degree centrality in the network structure.

H3. Degree centralities of Web 2.0 services show a power law distribution along the degree centralities at each time period t.

Pðk; tÞ , k2g ð5Þ

Analysis Data The lists containing information about Web 2.0 services and mashups from 1 September 2005 to the end of May 2007 were obtained from www.programmableweb. com. An average of 21 Web 2.0 services were listed and updated on the site during this

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period. Data included 445 Web 2.0 services and 1929 Web 2.0 mashups. However, 222 Web 2.0 services were removed from the analysis because they were isolated, that is no user utilised them for creating mashups during the study period. Thus only 223 Web 2.0 services were used to evaluate the hypotheses. Additionally we defined a blank Web 2.0 service, which represents a mashup that does not provide any Web 2.0 services. Thus the network that we analysed consisted of 224 nodes.

Network construction mechanism In order to apply linear regression to Hypothesis 1, equation (3) was transformed by the natural logarithm to equation (6), where a is a constant and t means a period:

ln rðtÞ ¼ a ln Rðt 2 1Þ þ a ð6Þ

The data were regressed monthly from October 2005 to May 2007. The observations in September 2005 were not considered because the accumulated shareness was not defined at that period. Table I shows the regression results for Hypothesis 1. The explanation power, R 2, averaged 0.321. The inclusion of a constant is appropriate in our model because R 2 was larger than the adjusted R 2. However, it can be ignored because the probability of a t-distribution was not significant at the 10 per cent level at each period. R 2 values were 0.166 in November 2005 and 0.149 in May 2007, which were small compared to those of other periods. The network may have been too immature to reveal the preferential attachment rule. The result of May 2007 is somewhat curious. R

2 values were 0.078 in December 2006 and 0.009 in January 2007,

both extremely small. In these two periods, two or three mashups combining many Web 2.0 services may have distorted the network structure. Excluding the four

YY-MM R 2 a a Sig. of a Sig. of a

05-October 0.4 20.731 0.909 0.548 0.027 05-November 0.166 22.235 0.307 0.018 0.148 05-December 0.326 21.672 0.511 0.04 0.021 06-January 0.395 21.837 0.525 0.005 0 06-February 0.428 21.771 0.525 0.003 0 06-March 0.512 21.481 0.57 0.006 0 06-April 0.357 22.16 0.44 0.001 0 06-May 0.265 22.145 0.464 0.001 0.001 06-June 0.619 20.62 0.785 0.28 0 06-July 0.347 22.192 0.383 0 0.001 06-Aug 0.376 21.675 0.509 0.013 0.002 06-September 0.342 21.886 0.514 0.005 0.001 06-October 0.45 21.441 0.637 0.014 0 06-November 0.448 22.178 0.465 0 0 06-December 0.078 23.267 0.277 0 0.05 07-January 0.009 24.473 0.094 0 0.533 07-February 0.246 22.277 0.435 0 0.001 07-March 0.247 22.081 0.522 0.002 0 07-April 0.26 22.274 0.433 0.001 0.001 07-May 0.149 22.712 0.429 0.001 0.007 Average 0.321 22.055 0.487 0.047 0.040

Table I. Regression results of equation (6) related to Hypothesis 1

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unusual periods when R 2 values were smaller than 0.2, the average R 2 increased to 0.376.

The exponent a averaged 0.487. In the periods when R 2 values were small, a values were very small compared to the average: 0.28 in December 2006 and 0.094 in January 2007. Eliminating these two periods, we see that a increased to 0.536, and they were all between 0.300 and 0.525. In 18 periods among 20 data points, a was significant at the 10 per cent level. The probability of t distribution averaged 0.04, which was significant at the 10 percent level. The probabilities of t distribution were 0.148 in November 2005 and 0.533 in January 2007, which were statistically insignificant. These two periods were included in the four periods of low explanation power. Excluding these four periods, the average probability of t distribution was 0.01, which was statistically significant at the 10 per cent level. Since the result excluding the four unusual periods augmented R 2 and the probability of t distribution only slightly, we included all the periods in the analysis.

Since Google is utilised for a large number of Web 2.0 services and it averaged 58 mashups per month for the period (1,156 mashups until May 2007), we investigated whether it was an outlier. In order to determine whether Google Maps distorted the structure of the network, the data sets were regressed without it. According to our results the average R 2 was 0.478, which was higher than in the original analysis. The exponent a and the probability of t-distribution were 0.791 and 0.000 on average, respectively. Google Maps did not lead to erroneous acceptance of Hypothesis 1. Our results supported Hypothesis 1. The exponent of equation (3) was 0.49:

rðtÞ , Rðt 2 1Þ0:49 ð7Þ

For testing Hypothesis 2 with a linear regression, equation (4) was transformed to equation (8), where b was a constant:

rðtÞ ¼ bD þ b ð8Þ

In Table II, the explanation power R 2 was 0.099 on average. Only five data sets out of 20 had R 2 values larger than 0.10. Only two data sets had R 2 values larger than 0.200. The probability of t-distribution averages 0.237. The dummy variable D was statistically insignificant at the 10 per cent level except in October 2005 when it was 0.013 and in December 2005 when it was 0.044. The explanation powers at these times were larger than 0.200. The magnitude of constant b and coefficient b were not explained because D was just a dummy variable. When Google Maps, the probable outlier, was removed the dummy variable was insignificant. Thus Hypothesis 2, which stated that the efforts of Web 2.0 service providers may improve node attributes, could be rejected.

Structure of the Web 2.0 service network Finally equation (5) representing Hypothesis 3 was transformed by the natural logarithm for linearisation, where c is a constant:

ln PðkÞ ¼ 2g ln k þ c ð9Þ

The degree centralities accumulated by each Web 2.0 service from September 2005 to May 2007 were calculated to understand the position and importance of each Web 2.0

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service (Table III). The exponent g in May 2007 was calculated to be 0.521. The result is sufficiently explained because R 2 was 0.604 and the probability of t-distribution was 0 in May 2007. However, it is different from the usual scale-free networks in which the exponent lies between 2 and 3. Figure 2 shows the distribution of degree centrality. The horizontal axis shows the degree centrality of each Web 2.0 service on the natural logarithm scale, and the vertical axis shows the number of nodes that had degree centrality in the natural logarithm scale. The points in the graph mark the empirical values. The estimated results from the empirical values are illustrated on a line in the graph. The pattern of the results indicates that the distribution of nodes with respect to degree centrality followed the power law. The dispersed region in the bottom right of the distribution is the result of noise caused by low probability (Štefančić and Zlatić, 2005).

In Table III, the regression showed good explanation power (average R2 ¼ 0:647). R

2 was larger than 0.600 for all but three periods: it was 0.441 in October 2005, 0.581 in November 2005 and 0.580 in February 2006. The regressions in the initial two periods may have had low explanation power because of the small number of links in the initial state. After that initial fluctuation the network evolved scale-free. The average g was 0.530, which was statistically significant at the 10 per cent level, and the probability of t-distribution averaged 0.002 except in the initial two periods (when it was zero). The g of 0.700 for September 2005 was high while the g of 0.459 for October 2005 was small. This initial-state fluctuation may have had the same cause as that of R 2 values in these time periods. The constant was included because the probability of t-distribution was zero on average. After the initial three periods were removed from the analysis, R 2 increased to 0.657 and g decreased to 0.525. In this

YY-MM R 2 b b Sig. of b Sig. of b

05-October 0.478 25.251 2.14 0 0.013 05-November 0.064 23.943 0.664 0 0.384 05-December 0.26 24.828 1.515 0 0.044 06-January 0.058 24.752 0.688 0 0.215 06-February 0.078 24.612 0.72 0 0.159 06-March 0.06 24.565 0.573 0 0.171 06-April 0.071 24.58 0.572 0 0.155 06-May 0.18 24.991 0.998 0 0.006 06-June 0.171 24.495 0.96 0 0.045 06-July 0.019 24.144 0.275 0 0.488 06-August 0.014 23.952 0.238 0 0.595 06-September 0.026 24.507 0.424 0 0.396 06-October 0.033 24.785 0.449 0 0.259 06-November 0.062 24.879 0.519 0 0.095 06-December 0.004 24.578 -0.175 0 0.644 07-January 0.003 25.055 0.158 0 0.699 07-February 0.147 24.915 0.801 0 0.01 07-March 0.169 25.316 0.992 0 0.002 07-April 0.034 24.682 0.414 0 0.252 07-May 0.053 25.144 0.568 0 0.114 Average 0.099 24.699 0.675 0 0.237

Table II. Regression results of equation (7) related to Hypothesis 2

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analysis all the periods were kept because these fluctuations had little influence on the results. To conclude, the results supported Hypothesis 3 and led to the following equation:

Pðk; tÞ , k20:53 ð10Þ

YY-MM R 2 c g Sig. of c Sig. of g

05-September 0.732 1.932 0.7 0.006 0.03 05-October 0.441 1.505 0.459 0.001 0.007 05-November 0.581 1.777 0.505 0 0 05-December 0.635 1.897 0.551 0 0 06-January 0.703 2.098 0.55 0 0 06-February 0.58 2.049 0.506 0 0 06-March 0.609 2.113 0.493 0 0 06-April 0.648 2.191 0.52 0 0 06-May 0.695 2.299 0.516 0 0 06-June 0.681 2.305 0.52 0 0 06-July 0.714 2.382 0.528 0 0 06-August 0.697 2.429 0.536 0 0 06-September 0.645 2.367 0.532 0 0 06-October 0.671 2.427 0.536 0 0 06-November 0.755 2.57 0.552 0 0 06-December 0.68 2.454 0.528 0 0 07-January 0.615 2.454 0.5 0 0 07-February 0.634 2.487 0.515 0 0 07-March 0.629 2.563 0.528 0 0 07-April 0.637 2.577 0.525 0 0 07-May 0.604 2.578 0.521 0 0 Average 0.647 2.260 0.530 0.000 0.002

Table III. Regression results of

equation (9) related to Hypothesis 3

Figure 2. The distribution of degree centralities for the Web 2.0

service network

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Discussion Scale-free Web 2.0 service network Regarding the structure of the network, Web 2.0 services and mashups are expected to evolve obeying the preferential attachment rule and the power law. One implication of a scale-free network is that a node can reach others efficiently through a few hubs. These efficient connections become clear as the network size increases. Each Web 2.0 service is involved in a variety of services provided by different companies. The small world phenomenon of Web 2.0 services indirectly shows that Web 2.0 evolved due to a combination of many services by some hubs such as Google Maps and Flickr. These key nodes indicate that creating Web 2.0 mashups follows a trend. For example, one of the current mashup trends is searching images (Flickr) and video clips (YouTube) on a map (Google Maps). The trend indirectly proves that Web 2.0 services evolve systematically, which is a desirable evolution pattern. The variety of Web 2.0 services created in the trend reflects user demand.

In view of technological fragility a heterogeneous structure may involve irrationality (Tu, 2000). From a technological perspective a scale-free Web 2.0 service network contains structural fragility because many services depend on a few Web 2.0 services. This architecture requires a stable operation of Web 2.0 service providers, especially key players. For example, almost half of all mashups will fail if the server of Google Maps, a hub, is out of order. If the cost of operating a few large Web 2.0 service providers is smaller than those of a homogenous network, the scale-free network is a desirable outcome.

In terms of competition the Web 2.0 service network may not be so desirable because a majority of Web 2.0 services depend on a few hub Web 2.0 services. However, the relationships between Web 2.0 services are both competitive and complementary. Any hub Web 2.0 service needs other Web 2.0 services whether they are hubs or not. Even Web 2.0 services in the same service category need each other. For example, the Web 2.0 mashup ACME GeoRSS Map Viewer utilises both Google Maps and Yahoo! Maps. We conclude that heterogeneity of degree distribution contributes to the progress of the system in which a few Web 2.0 services lead and a majority of Web 2.0 services follow.

The low level exponent in the preferential attachment rule and the scale-free network presents an interesting issue. In prior research a linear preferential equation generally led to the scale-free network with nearly 2 , g , 3 (Barabási et al., 2001; Fu et al., 2008; Krapivsky et al., 2000). However, our results show a ¼ 0:49 for Hypothesis 1 and g ¼ 0:53 for Hypothesis 3. This low exponent of the scale-free network appears in other studies as well. The exponent in the page network of Wikipedia is smaller than 2 although the network seems to be scale-free (Hendler et al., 2008). Moreover, for the tag network of Flickr data the exponent was smaller than 1 although the network seems to be scale-free (Angus et al., 2008). This unusually low exponent should be investigated since it indicates that the evolution of the Web 2.0 service network may have some additional mechanisms affecting the building of a scale-free network.

Ranking of top Web 2.0 services Despite the small initial variations the preferential attachment rule tends to widen the distribution inequality and then keeps the centrality ranking from changing. In the Web 2.0 service network, Web 2.0 services ranking in the top five with regard to accumulated degree centrality show this tendency (Table IV). The top five rankings

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centrality

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were invariant in the study period – Google Maps maintained the top position and only eight other Web 2.0 services occupied the top five spots. Among them delicious, Flickr and Amazon eCommerce entered the top five ranking 22, 20 and 19 times respectively during the study period. If the ranking had changed randomly, then 105 Web 2.0 services could ideally have occupied the top five spots in the study period. The ranking of Amazon eCommerce dropped from the top two between October 2005 and February 2006 to the top three between March 2006 and May 2007. The ranking of Flickr showed a tendency to improve in the initial period and maintained second place from March 2006 to the end of the study period. This implies that Web 2.0 service linkages in the Web 2.0 service network may depend on a variety of factors, such as quality improvement of services due to Web 2.0 service providers’ efforts, and trend changes due to market context, as well as the classic preferential attachment rule caused by visibility and network externality. The interplay of multiple factors induces a smooth change under a stable structure.

The position of Google Maps at the top spot is peculiar. Considering the advantage of the first mover, Google Maps should have followed Amazon eCommerce because Amazon released its Web 2.0 services in 2003 and Google Maps released its Web 2.0 services in June 2005 (Roush, 2005). This peculiarity can be explained by users who started using geographic searches, or “browser for the earth”, instead of keyword searches (Roush, 2005, p. 56). This phenomenon shows that the Web 2.0 service network reflects changes in market context. Mashups made with Web 2.0 services with open APIs encourage the combination of users’ innovative resources with excellent web service functions and data, such as maps, to yield rich innovation in a variety of content (Rouse et al., 2007). Such creativity is the realisation of a network of inventive minds meeting in cyberspace (DeBresson and Amesse, 1991; Freeman, 1991).

Conclusion In this paper the structure of the Web 2.0 service network and the rules of its evolution were analysed. The results suggest that the structure has evolved into a scale-free network following the preferential attachment rule. However, the values of the exponents in our results differ from those in typical preferential attachment and scale-free systems. A network with low exponents such as ours is likely to fluctuate due to changes in external contexts.

The findings suggest further studies in this field. First, several evaluations should be conducted in order to thoroughly establish the model. These evaluations should deal with time correlation between the introduction of Web 2.0 services and mashups, cumulative probability for removing noise in low probability scenarios, and the preferences categorised by acquaintances (Davidsen et al., 2002; Newman, 2001; Štefančić and Zlatić, 2005). Finally some qualitative analysis is necessary. So far this research has focused on quantitative analysis (especially degree centrality) to explain the network’s self-organisation. Qualitative analysis is needed to determine which elements affect the interconnection of nodes and whether the network is open.

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About the authors Junseok Hwang is an Associate Professor in the Technology Management, Economics and Policy Programme at Seoul National University in Korea. Prior to this, he was an Assistant Professor in the School of Information Studies at Syracuse University. He has been teaching courses in computer networks, telecommunications, telecommunication policy, network modelling and analysis. He received his PhD in Information Science and Telecommunications from the University of Pittsburgh and a Master’s degree in Telecommunications from the University of Colorado, Boulder.

Jörn Altmann is an Associate Professor in the Technology Management, Economics and Policy Programme at Seoul National University. Prior to this, he taught courses in computer networks at UC Berkeley, worked as a Senior Scientist at Hewlett-Packard Labs, and has been a postdoctoral fellow at EECS and ICSI of UC Berkeley. He received his BSc degree, his MSc degree and his PhD from the University of Erlangen-Nuremberg. His current research centres on internet economics, with a focus on the economics of internet services and on integrating economic models into internet infrastructures.

Kibae Kim is a PhD student in the Technology Management, Economics and Policy Programme at Seoul National University. Kibae Kim is the corresponding author and can be contacted at: [email protected]

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