Week 5: social network & measures Flashcards
What is the social brain hypothesis?
There is a correlation between brain size ang group size
What are the three degrees of influence?
Behaviour is influenced by peer, peer of peer and peer of peer of peer
What is Aij in a directed graph adjacency matrix?
When Aij=1, there is an edge from j to i
What is an acyclic network?
A directed network with no cycles. A cycle is a closed loop of edges with arrows pointing the same way.
What is a bipartite network?
Network with two kinds of nodes and edges that run only between nodes of different kinds
What are bipartite networks often used for?
Representing membership of groups
What are 6 types of node-level metrics?
Degree, degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, page rank
What is the degree of a node?
The number of edges it has connected to it. Also indegree and outdegree
What is degree centrality?
The number of nodes adjacent to a given node
What is closeness centrality?
The inverse of the mean shortest distances from i to every other node in the network
What is betweenness centrality?
Number of times a node lies on the shortest path between two other nodes
What does betweenness centrality represent?
Nodes with high betweenness centrality are often important controllers of power or information
What is eigenvector centrality?
How central a node is depends on how central its neighbouring nodes are (weighted sum of the centralities of neighbouring nodes)
What is page rank?
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
What are 6 network-level metrics?
Degree distribution, density, centralisation, components, communities, clustering
What is degree distribution?
The distribution of how to summarise the degree of all nodes of a network
What is the density of a network
The number of actual ties (m), divided by the number of possible ties in a network
How to calculated the density of directed and undirected networks?
d(directed) = m/(n(n–1)) d(undirected) = m/(n(n–1)/2)
What does the density of a network tell us
Tells us about the redundancy of connections
What happens to the density of a sparse network?
The density approaches 0 as n increases
What is the centralisation of a network?
The extent to which a network revolves around a single node
How is centralisation measured?
Standard deviation = (mean of degrees of all node – degrees of each node)^2 /n
What is the diameter of a network?
The longest of the shortest path between two nodes
What are components?
Clusters that are not connected to each other, there is no path between any pair of nodes in different components
What is a connected network?
A network with only one component
What are strongly connected nodes?
Nodes A and B are strongly connected if there is a directed path from A to B and B to A
What are weakly connected nodes?
A and B are weakly connected if there is only a path between them in one direction
What is a strongly connected component?
A component that contains strongly connected nodes
What is an out-component?
The set of nodes that are reachable via directed paths starting from a specified node A, and including A itself
What is an in-component?
The set of all nodes from which there is a directed path to A, including A itself
What is a k-component?
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
What are node-independent paths?
Two paths are node-independent if they share none of the same nodes except the starting and ending nodes
What is a community?
Parts of the network in which the nodes are more connected to each other than to the rest of the network
How do you find communities?
Community detection algorithms, you can use many criteria to design community detection algorithms
What is an example of a real-world community?
Opinion-based communities: echo chambers - an environment where a person only encounters information or opinions that reflect and reinforce their own
What is the local clustering coefficient of a node?
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
What is the global clustering coefficient of a network?
Counts the percentage of closed triangles in the whole network
What is another name for clustering coefficient?
Transitivity
What is transitivity in a network?
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
What is partial transitivity?
Partial transitivity means that if u knows v and v knows w, it is more likely that u knows w
What is a closed path?
A path is closed if it forms a loop
What are two equations for the clustering coefficient of a network?
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
What is the equation for the local clustering coefficient?
For node i, Ci = number of pairs of neighbours of i that are connected/number of pairs of neighbours of i
What is local clustering correlated with?
Local clustering and betweenness centrality are strongly correlated
What is the redundancy of a node i?
The mean number of connections from a neighbour of i to other neighbours of i
