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# Table 1 Definitions and descriptions of network metrics

Network metrics | Definitions | Descriptions |
---|---|---|

Measures of segregation | ||

Clustering coefficient (Cp) | \( {L}_p=\frac{1}{N\left(N-1\right)}\sum \limits_{i\in G}\sum \limits_{j\in G,j\ne i}{L}_{ij} \) | L_{ij} is the shortest path length between nodes i and j, N is the set of all nodes in the network G. |

Local efficiency (Eloc) | \( {E}_{local}=\frac{1}{N}\sum \limits_{i\in G}{E}_{local,i} \) | E_{local, i} is the local efficiency of node i. |

Measures of integration | ||

Characteristic path length (Lp) | \( {C}_p=\frac{1}{N}\sum \limits_{i\in G}\frac{2\ast {E}_i}{k_i\left({k}_i-1\right)} \) | k_{i} is the degree of node i, E_{i} 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 L_{p}. |

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. |