Table 1 Indicators for social network analysis.

Network Density

Network density is the ratio of connections between network nodes to the maximum number of links in the entire network. The network density measures how closely the nodes are connected.

\(D = {\textstyle{{2m} \over {n(n - 1)}}}\)

Where: D is network density; m is the sum of the number of connections in the relational network; n is the number of actors.

Average Distance

The average distance is the mean value of the optimal path among all nodes and indicates the efficiency of information transfer. The smaller the indicator’s worth, the better the accessibility of the network.

\(L = 2{\textstyle{{\mathop {\sum}\nolimits_{i \ne j} {dij} } \over {n(n - 1)}}}\)

Where: L is the average distance; d_ij is the shortest path length between i and j; n is the number of actors.

Core-Periphery

Based on the closeness between different nodes in the social network, the nodes can be divided into core and periphery zones. Nodes in the core occupy a more important position in the overall social network.

Small Cliques

Cliques, also called cohesive subgroups, are analyzed as collections of well-connected actors in a network. It divides the small groups formed within the network with strong ties, which helps to reveal the substructure situation within the network.

Degree Centrality

Degree Centrality is the ability to communicate and interact directly with other stakeholders—the greater the degree of centrality, the higher the position in the relationship network and the greater the power.

\(C_{RDi} = {\textstyle{{\mathop {\sum}\nolimits_{j = 1}^n {xij} } \over {n - 1}}}\)

Where: C_RDi is degree centrality; x_ij is either 0 or 1. If i and j are connected, x_ij is 1. Otherwise, it is 0; n is the number of actors.

Betweenness Centrality

Betweenness centrality represents the spacing between stakeholders—the higher the betweenness centrality, the greater its ability to control resources.

\(C_{RBi} = {\textstyle{{2\mathop {\sum}\nolimits_{j < {{{\mathrm{k}}}}} {{\textstyle{{gjk(i)} \over {gjk}}}} } \over {(n - 1)(n - 2)}}}\)

Where: C_RBi is betweenness centrality; g_jk(i) is the number of shortest paths where nodes j and k are connected and pass through node i; g_ik is the number of shortest paths where j and k are connected; n is the number of actors.

Closeness Centrality

Closeness centrality represents the sum of each stakeholder’s distance from other stakeholders. The smaller the closeness centrality, the lower its dependence and the higher its independence.

\(C_{RPi} = {\textstyle{{n - 1} \over {\mathop {\sum}\nolimits_{j \in N} {dij} }}}\)

Where: C_RPi is closeness centrality, d_ij is the shortest path length between i and j; n is the number of actors.