# Table 1 Definitions and descriptions of network metrics

Network metricsDefinitionsDescriptions
Measures of segregation
Clustering coefficient (Cp)$${L}_p=\frac{1}{N\left(N-1\right)}\sum \limits_{i\in G}\sum \limits_{j\in G,j\ne i}{L}_{ij}$$Lij is the shortest path length between nodes i and j, N is the set of all nodes in the network G.
Local efficiency (Eloc)$${E}_{local}=\frac{1}{N}\sum \limits_{i\in G}{E}_{local,i}$$Elocal, i is the local efficiency of node i.
Measures of integration
Characteristic path length (Lp)$${C}_p=\frac{1}{N}\sum \limits_{i\in G}\frac{2\ast {E}_i}{k_i\left({k}_i-1\right)}$$ki is the degree of node i, Ei is the number of edges that consists of the neighbors of node i.
Global efficiency (Eglob)$${E}_{glob}=\frac{1}{N\left(N-1\right)}\sum \limits_{i\in G}\sum \limits_{j\in G,j\ne i}\raisebox{1ex}{1}\!\left/ \!\raisebox{-1ex}{{L}_{ij}}\right.$$It is inversely related to Lp.
Other concepts
Small-worldness (σ)$$\upsigma =\frac{L_p/{L}_{ran}}{C_p/{C}_{ran}}$$σ measures small-worldness. Cran and Lran were averaged from 100 matched random networks.
1. Cran, clustering coefficient for a random network; Lran, characteristic for a random network 