Week 5: social network & measures

Question 1

What is the social brain hypothesis?

Answer 1

There is a correlation between brain size ang group size

Question 2

What are the three degrees of influence?

Answer 2

Behaviour is influenced by peer, peer of peer and peer of peer of peer

Question 3

What is Aij in a directed graph adjacency matrix?

Answer 3

When Aij=1, there is an edge from j to i

Question 4

What is an acyclic network?

Answer 4

A directed network with no cycles. A cycle is a closed loop of edges with arrows pointing the same way.

Question 5

What is a bipartite network?

Answer 5

Network with two kinds of nodes and edges that run only between nodes of different kinds

Question 6

What are bipartite networks often used for?

Answer 6

Representing membership of groups

Question 7

What are 6 types of node-level metrics?

Answer 7

Degree, degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, page rank

Question 8

What is the degree of a node?

Answer 8

The number of edges it has connected to it. Also indegree and outdegree

Question 9

What is degree centrality?

Answer 9

The number of nodes adjacent to a given node

Question 10

What is closeness centrality?

Answer 10

The inverse of the mean shortest distances from i to every other node in the network

Question 11

What is betweenness centrality?

Answer 11

Number of times a node lies on the shortest path between two other nodes

Question 12

What does betweenness centrality represent?

Answer 12

Nodes with high betweenness centrality are often important controllers of power or information

Question 13

What is eigenvector centrality?

Answer 13

How central a node is depends on how central its neighbouring nodes are (weighted sum of the centralities of neighbouring nodes)

Question 14

What is page rank?

Answer 14

Variant of eigenvector centrality, used by google. Having links to you from other important nodes increases your centrality, but if that important node sends out a lot of links, the importance passed on to you is weighted less

Question 15

What are 6 network-level metrics?

Answer 15

Degree distribution, density, centralisation, components, communities, clustering

Question 16

What is degree distribution?

Answer 16

The distribution of how to summarise the degree of all nodes of a network

Question 17

What is the density of a network

Answer 17

The number of actual ties (m), divided by the number of possible ties in a network

Question 18

How to calculated the density of directed and undirected networks?

Answer 18

d(directed) = m/(n(n–1))
d(undirected) = m/(n(n–1)/2)

Question 19

What does the density of a network tell us

Answer 19

Tells us about the redundancy of connections

Question 20

What happens to the density of a sparse network?

Answer 20

The density approaches 0 as n increases

Question 21

What is the centralisation of a network?

Answer 21

The extent to which a network revolves around a single node

Question 22

How is centralisation measured?

Answer 22

Standard deviation = (mean of degrees of all node – degrees of each node)^2 /n

Question 23

What is the diameter of a network?

Answer 23

The longest of the shortest path between two nodes

Question 24

What are components?

Answer 24

Clusters that are not connected to each other, there is no path between any pair of nodes in different components

Question 25

What is a connected network?

Answer 25

A network with only one component

Question 26

What are strongly connected nodes?

Answer 26

Nodes A and B are strongly connected if there is a directed path from A to B and B to A

Question 27

What are weakly connected nodes?

Answer 27

A and B are weakly connected if there is only a path between them in one direction

Question 28

What is a strongly connected component?

Answer 28

A component that contains strongly connected nodes

Question 29

What is an out-component?

Answer 29

The set of nodes that are reachable via directed paths starting from a specified node A, and including A itself

Question 30

What is an in-component?

Answer 30

The set of all nodes from which there is a directed path to A, including A itself

Question 31

What is a k-component?

Answer 31

A k-component is a set of nodes such that each is reachable from each of the others by at least k node-independent paths

Question 32

What are node-independent paths?

Answer 32

Two paths are node-independent if they share none of the same nodes except the starting and ending nodes

Question 33

What is a community?

Answer 33

Parts of the network in which the nodes are more connected to each other than to the rest of the network

Question 34

How do you find communities?

Answer 34

Community detection algorithms, you can use many criteria to design community detection algorithms

Question 35

What is an example of a real-world community?

Answer 35

Opinion-based communities: echo chambers - an environment where a person only encounters information or opinions that reflect and reinforce their own

Question 36

What is the local clustering coefficient of a node?

Answer 36

Quantifies how close its neighbours are to being fully connected. The average probability that a pair of i’s friends are friends of one another

Question 37

What is the global clustering coefficient of a network?

Answer 37

Counts the percentage of closed triangles in the whole network

Question 38

What is another name for clustering coefficient?

Answer 38

Transitivity

Question 39

What is transitivity in a network?

Answer 39

Transitivity in a network means that if node u is connected to node v any v is connected to w, then u is also connected to w

Question 40

What is partial transitivity?

Answer 40

Partial transitivity means that if u knows v and v knows w, it is more likely that u knows w

Question 41

What is a closed path?

Answer 41

A path is closed if it forms a loop

Question 42

What are two equations for the clustering coefficient of a network?

Answer 42

``` C = number of closed paths of length two/number of paths of length two C = number of triangles*6/number of paths of length two ```

Question 43

What is the equation for the local clustering coefficient?

Answer 43

For node i, Ci = number of pairs of neighbours of i that are connected/number of pairs of neighbours of i

Question 44

What is local clustering correlated with?

Answer 44

Local clustering and betweenness centrality are strongly correlated

Question 45

What is the redundancy of a node i?

Answer 45

The mean number of connections from a neighbour of i to other neighbours of i