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Table 1 Definitions and descriptions of network metrics

From: Altered structural brain networks at term-equivalent age in preterm infants with grade 1 intraventricular hemorrhage

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