Subgraph Centrality

Subgraph Centrality

• Accounts for the participation of a node in all subgraphs of the network
• Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network motifs (1)
• Measures density of eigenvalues within the network’s adjacency matrix A
• SC(i) = SUM^∞_t=0μ_t(i) / t! where μ_t(i) is the number of paths starting and ending with node i of length t and can be calculated by μ_t(i) = (A^k)_ii
• This boils down to SC(i) = (e^A)_ii where e^A is the matrix exponential of A

For more Information:

1. Subgraph Centrality in Complex Networks
2. Introduction to Graph Theory