Table 2 Metrics using external connectivity for dynamic community evolution

Inter-community edges

\(E_{inter}\)

Number of edges on the boundary of C

Expansion

\(\frac{E_{inter}}{n_c}\)

Number of edges per node that point outside the community

Cut ratio

\(\frac{E_{inter}}{n_c\left( n-n_c\right) }\)

Fraction of existing edges (out of all possible edges) leaving the community, where n is total number of vertices