Table 1.

Definitions of the statistical characteristics used for network analysis in this study.

Statistical characteristic	Symbol	Equationa,b,c,d	Description
Degree	k	$k_i={\sum }_{j=1}^{\mathrm{N}}{e}_{\text{ij}}$	The total number of edges for a node i
Average degree	<k>	$<k>=\frac{{\sum }_{i=1}^N{k}_{\mathrm{i}}}{N}$	The average degree of the network
Average path length	L	$L=\frac{1}{N(N-1)}{\sum }_{i\ne j}{d}_{\text{ij}}$	The mean distance between two nodes, averaged over all pairs of nodes
Diameter	D	D = max{dij}	The maximum distance between any pair of nodes
Clustering coefficient	C	$C_i=\frac{2{\mathrm{e}}_i}{k_i(k_i-1)}(k_i\ge 2)$	The probability that two nodes are linked to each other given that they are both connected to node i
Degree centrality	Cd	$C_{\mathrm{d}}=\frac{k_i}{N-1}$	The proportion of other nodes that are adjacent to node i
Betweenness centrality	Cb	$C_{\mathrm{b}}={\sum }_{j(<k)}^N{\sum }_k^N\frac{g_{\text{jk}}(i)}{g_{\text{jk}}}$	The proportion of all geodesics between pairs of other nodes that include this node i
Closeness centrality	Cc	$C_{\mathrm{c}}=\frac{N-1}{{\sum }_{j=1}^N{d}_{\text{ij}}}$	The number of other nodes divided by the sum of the distances between the node i and all the other nodes

^ae_ij is the numbers of edges from node i to j.

^bd_ij is the shortest path length from node i to j.

^cN is the total number of nodes in the network.

^dg_jk is the numbers of geodesics connecting nodes j and k.