Table 1.
Formal Definitions of Metrics Used in Graph Analysis
FormulaSpecifications
Modularity (QQ = $∑i,jN$[Aij − γPij]δ(ci, cjAij: observed number of connections between nodes i and j
Pij: predicted number of connections between nodes i and j
N: number of nodes in the whole network
ci: module in which the node i is included
δ(ci, cj): Kronecker delta function is equal to 1 if ci = cj, 0 otherwise
γ: resolution parameter
Predicted number of connections (PijPij = $kikj2m$ ki: the degree of the node i
m: total number of edges in the network
Participation coefficient (PCPCi = 1 − $∑sMkiski2$ M: number of modules
kis: number of connections of node i to nodes in module s
FormulaSpecifications
Modularity (QQ = $∑i,jN$[Aij − γPij]δ(ci, cjAij: observed number of connections between nodes i and j
Pij: predicted number of connections between nodes i and j
N: number of nodes in the whole network
ci: module in which the node i is included
δ(ci, cj): Kronecker delta function is equal to 1 if ci = cj, 0 otherwise
γ: resolution parameter
Predicted number of connections (PijPij = $kikj2m$ ki: the degree of the node i
m: total number of edges in the network
Participation coefficient (PCPCi = 1 − $∑sMkiski2$ M: number of modules
kis: number of connections of node i to nodes in module s
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