Table 1 Network indicators

Indicator Description Formula
Degree of centrality Number of links incident upon a node $${C}_d(G)=\frac{{\displaystyle \sum_{i=1}^NCd\left({v}^{*}\right)-Cd(vi)}}{H}$$
CD (g): degree centrality
v * : node with the highest centrality degree
Vi:node i
Index of centralization The degree to which a network is organized around a point. $${C}_d=\frac{{\displaystyle \sum_{i=1}^N\left(C \max - Ci\right)}}{ \max \left[{\displaystyle \sum_{i=1}^N\left(C \max - Ci\right)}\right]}$$
C max :centrality focal node
Ci = centrality rest of nodes
Degree of intermediation Possibility of a node to mediate between pairs of nodes $${C}_b=\frac{2{\displaystyle \sum_{i=1}^g\left[Cb\left({n}^{*}\right)-Cb\left({n}_i\right)\right]}}{\left[\left(g-1\Big){}^2\left(g-2\right)\right)\right]}$$
Cb(n*):highest intermediation between agents
g: number of nodes
Degree of closeness Average distance of each agent in respect of other agents. $${C}_c={\displaystyle \sum_{x\in V-C}df\left(x,C\right)}$$
X:node x
Density Existing links in relation to possible links. $$D=\frac{{\displaystyle \sum_{i=1}^N{\displaystyle \sum_{j=1}^NXij}}}{n\left(n-1\right)}$$