Table 3 Metrics using both internal and external connectivity for dynamic community evolution

Normalized cut

\(\frac{E_{inter}}{2E_{intra}+E_{inter}} + \frac{E_{inter}}{2(E-E_{intra})+E_{inter}}\)

Computes the cut cost as a fraction of the total edge connections to all the nodes in the graph

Conductance

\(\frac{E_{inter}}{2E_{intra}+E_{inter}}\)

Fraction of total edge volume that points outside the community

Clustering coefficient

\(CC(v)=\frac{e_i}{\left( {\begin{array}{c}D(v)\\ 2\end{array}}\right) }\)

Measures the “clumpiness” of a graph, the ratio of the existing edges and the total number of possible edges among the neighbors of a node. Where, \(e_i:\) number of edges between the neighbors, and \(\left( {\begin{array}{c}D(v)\\ 2\end{array}}\right) :\) the total number of possible connections among the neighbors

Separability

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

Measures the ratio between the internal and the external number of edges on the boundary of C