homework

POLI 100F Lecture 2: Social Network Mechanics

Gregoire Phillips

University of California, San Diego

[email protected]

October 12, 2020

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Overview

1 Announcements

2 Social Network Structures

3 Centrality

4 Clustering

5 Wrap-Up

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 2 / 38

A few brief reminders

Try to get required readings done before watching lecture

Readings with triple asterisks are recommended, but not required, readings

We may engage with both in the lecture, but will only expect you to be familiar with what is required

No participation quiz this week (because we still have people adding the course)

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 3 / 38

Review: What is a social network?

Social networks describe connections built on social interactions, relationships, associations, and influence

The simplest network is a dyad, or pair of individuals

Sometimes, these dyads agglomerate to form large, interconnected web structures

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 4 / 38

Review: What is a social network?

Social networks describe connections built on social interactions, relationships, associations, and influence The simplest network is a dyad, or pair of individuals

Sometimes, these dyads agglomerate to form large, interconnected web structures

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 4 / 38

Review: What is a social network?

Social networks describe connections built on social interactions, relationships, associations, and influence The simplest network is a dyad, or pair of individuals

Sometimes, these dyads agglomerate to form large, interconnected web structures

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 4 / 38

Social network mechanics

A network is defined by a set of “nodes” and all “links” that connect pairs of them.

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Social network mechanics

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Social network mechanics

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Social network mechanics

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Social network mechanics

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Social network mechanics

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Social network mechanics

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Social network mechanics

This one isn’t useful if we want to learn something from the visual Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 12 / 38

Social network mechanics

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Social network mechanics

Links can be undirected or directed Directed links can be unidirectional or bidirectional

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Social network mechanics

We can think of networks mathematically as lists of edges linking nodes

We call this an edgelist

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Social network mechanics

Finally, we can think of networks as matrices (in math, not science fiction)

We can represent them with something called an “adjacency matrix”

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Social network mechanics

Finally, we can think of networks as matrices (in math, not science fiction)

We can represent them with something called an “adjacency matrix”

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 17 / 38

Social network mechanics

Finally, we can think of networks as matrices (in math, not science fiction)

We can represent them with something called an “adjacency matrix”

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 18 / 38

Social network mechanics

How do we think about network size?

One way we talk about this is network diameter

To understand this, let’s talk about walks and paths

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 19 / 38

Social network mechanics

How do we think about network size?

One way we talk about this is network diameter

To understand this, let’s talk about walks and paths

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 19 / 38

Social network mechanics

How do we think about network size?

One way we talk about this is network diameter

To understand this, let’s talk about walks and paths

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 19 / 38

Social network mechanics

Walk: sequence of nodes connected by links. We can “walk” from node to node along links

Path: sequence of nodes connected by links that does not repeat any nodes (except maybe the first and last)

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 20 / 38

Social network mechanics

Walk: sequence of nodes connected by links. We can “walk” from node to node along links

Path: sequence of nodes connected by links that does not repeat any nodes (except maybe the first and last)

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 20 / 38

Social network mechanics

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Social network mechanics

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Social network mechanics

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Social network mechanics

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Social network mechanics

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Social network mechanics

Number of links traversed in this walk: 6

But how can we use walks to measure networks?

Answer: measure the shortest walk, or the network diameter

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Social network mechanics

Number of links traversed in this walk: 6

But how can we use walks to measure networks?

Answer: measure the shortest walk, or the network diameter

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 26 / 38

Social network mechanics

Number of links traversed in this walk: 6

But how can we use walks to measure networks?

Answer: measure the shortest walk, or the network diameter

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 26 / 38

Social network mechanics

Number of links traversed in this walk: 2 This network’s diameter is not 2, though. We need the longest shortest path What is it?

It’s 3. Longest shortest path is from 1-5.

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 27 / 38

Social network mechanics

Number of links traversed in this walk: 2 This network’s diameter is not 2, though. We need the longest shortest path What is it? It’s 3. Longest shortest path is from 1-5.

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Social network mechanics

Network Diameter

Length of the longest shortest path in the network

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Social network mechanics

Now we have 2 components to our network

What is this network’s diameter?

Answer: 3 – longest shortest path

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Social network mechanics

Now we have 2 components to our network

What is this network’s diameter?

Answer: 3 – longest shortest path

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 29 / 38

Social network mechanics

Now we have 2 components to our network

What is this network’s diameter?

Answer: 3 – longest shortest path

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 29 / 38

Social network mechanics

We can now describe network nodes, links/ties, and size.

But how do we measure the connectedness of individuals within networks?

Another way of thinking about this: how do we measure a node’s importance within a network?

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Social network mechanics

We determine a node’s importance within a network by measuring it’s centrality. We can measure this several ways:

Total number of direct connections (“degree” centrality)

How close a node is to all other nodes (“closeness” centrality )

How many “shortest paths” cross through a node? (“betweenness centrality”)

How close is a node to other important nodes (“eigenvector centrality”)

Let’s break down two of these in detail: degree and closeness centrality

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Social network mechanics

To calculate degree centrality, count the number links coming directly from the node in question

Then divide this number by the number of nodes, n, minus 1

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Social network mechanics

Closeness centrality is a bit more complex

To calculate this, count the number of nodes and subtract 1 again

Then take the sum of the number of links separating the node in question from each other node in the network

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 33 / 38

Social network mechanics

Closeness centrality is a bit more complex

To calculate this, count the number of nodes and subtract 1 again

Then take the sum of the number of links separating the node in question from each other node in the network

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 33 / 38

Social network mechanics

Closeness centrality is a bit more complex

To calculate this, count the number of nodes and subtract 1 again

Then take the sum of the number of links separating the node in question from each other node in the network

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 33 / 38

Social network mechanics

So now we have an idea of what centrality is

But centrality doesn’t really tell us about how “dense” a network is

How many of a given node’s friends are also friends with each other?

This is called clustering

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Social network mechanics

So now we have an idea of what centrality is

But centrality doesn’t really tell us about how “dense” a network is

How many of a given node’s friends are also friends with each other?

This is called clustering

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 34 / 38

Social network mechanics

So now we have an idea of what centrality is

But centrality doesn’t really tell us about how “dense” a network is

How many of a given node’s friends are also friends with each other?

This is called clustering

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 34 / 38

Social network mechanics

So now we have an idea of what centrality is

But centrality doesn’t really tell us about how “dense” a network is

How many of a given node’s friends are also friends with each other?

This is called clustering

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 34 / 38

Social network mechanics

This is what clustering looks like, in math.

(Don’t worry – we aren’t going to do math)

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Social network mechanics

This is what clustering looks like, in math.

(Don’t worry – we aren’t going to do math)

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 35 / 38

Social network mechanics

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 36 / 38

Social network mechanics

We now have an understanding of

How networks are structured

How to measure distance in a network

How to measure the importance of nodes within a network through centrality

How to measure “closeness” through clustering

We will return to other concepts of centrality and clustering as we encounter them, but we now have enough basic knowledge and language to describe networks and their impact on behavior

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 37 / 38

Social network mechanics

We now have an understanding of

How networks are structured

How to measure distance in a network

How to measure the importance of nodes within a network through centrality

How to measure “closeness” through clustering

We will return to other concepts of centrality and clustering as we encounter them, but we now have enough basic knowledge and language to describe networks and their impact on behavior

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 37 / 38

Social network mechanics

We now have an understanding of

How networks are structured

How to measure distance in a network

How to measure the importance of nodes within a network through centrality

How to measure “closeness” through clustering

We will return to other concepts of centrality and clustering as we encounter them, but we now have enough basic knowledge and language to describe networks and their impact on behavior

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 37 / 38

Social network mechanics

We now have an understanding of

How networks are structured

How to measure distance in a network

How to measure the importance of nodes within a network through centrality

How to measure “closeness” through clustering

We will return to other concepts of centrality and clustering as we encounter them, but we now have enough basic knowledge and language to describe networks and their impact on behavior

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 37 / 38

Social network mechanics

We now have an understanding of

How networks are structured

How to measure distance in a network

How to measure the importance of nodes within a network through centrality

How to measure “closeness” through clustering

We will return to other concepts of centrality and clustering as we encounter them, but we now have enough basic knowledge and language to describe networks and their impact on behavior

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 37 / 38

Social network mechanics

Over the next two weeks, we’re going to dive into:

Social networks and health (Week 3)

Social networks and our social lives (Week 4)

See you then!

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 38 / 38

Social network mechanics

Over the next two weeks, we’re going to dive into:

Social networks and health (Week 3)

Social networks and our social lives (Week 4)

See you then!

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 38 / 38

Social network mechanics

Over the next two weeks, we’re going to dive into:

Social networks and health (Week 3)

Social networks and our social lives (Week 4)

See you then!

Gregoire Phillips (UCSD) Social Data Analysis October 12, 2020 38 / 38