Skip to Main Content
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 
Close Modal

or Create an Account

Close Modal
Close Modal