The sum of the weights of all edges containing node i
Eccentricity
The maximum distance from node i to any other node
Closeness centrality
The reciprocal of the sum of the shortest distances from node i to all other nodes
Harmonic closeness centrality
The number of pairs of distinct nodes j; k both different from node i for which the shortest path between j and k passes through node i
Betweenness centrality
The number of pairs of distinct nodes j; k both different from node i for which the shortest path between j and k passes through node i
Hub score
Let be the adjacency matrix of the network. The hub score of node i is the i th component of the eigenvector corresponding to the maximum eigenvalue of
Authority score
It equals to the weighted sum of its neighbours’ hub score. That is,
Local clustering coefficient
It is given by the proportion of links between the vertices within node i’s neighbourhood divided by the number of links that could possibly exist between them
Eigen centrality1
The same as hub score except for we use the matrix adjacency matrix a instead of here
FRI
Indegree
The number of number of edges ending at node i
Outdegree
The number of number of edges starting at node i
Weighted indegree
The sum of the weight of all edges ending at node i
Weighted outdegree
The number of number of edges ending at node i
Eccentricity
Same as
Closeness centrality
Same as
Harmonic closeness centrality
Same as
Betweenness centrality
Same as
Hub score
Same as
Authority score
Same as
Page rank coefficient
An algorithm introduced by Google to rank web pages. It does so by estimating the probability that a person randomly clicking on links will arrive at the given page
Local clustering coefficient
It is given by the proportion of links between the vertices within node’s neighbourhood divided by the number of links that could possibly exist between them
