In order to choose a network-based measure of firms' GIC, multiple global network metrics, partially overlapping with the concept of network activation, have been considered.
Density
The Density (D ) refers to the number of relationships within the network and measures the actual number of edges over the maximum possible number of edges within a given network (Freeman et al., 1979; Wasserman & Faust, 1994). The Density shows values ranging from 0 to 1, where extreme scores correspond to a null (i.e., edgeless) graph and a complete (fully-connected) graph, respectively. However, although this metric provides a snapshot on nodes tendency to relate to each other, it does not consider the edge weights, resulting in a significant loss of information concerning the strength of nodes’ relationship.
Global Clustering Coefficient
A more complex metric referring to the number of edges between groups of nodes is the Global Clustering Coefficient (Wasserman & Faust, 1994; Barrat et al., 2004), or Global Transitivity, which provides an average rating of nodes' tendency to form triangles in the network (Local Clustering Coefficient). Unlike Density, several variants of the CCmetric have been proposed to deal with weighted networks (Barrat et al., 2004; Zhang & Horvath, 2005; Kalna & Higham, 2006; Picciolo, F. et al., 2022), thus including edge weight information in the calculation of the global transitivity score. For this study, it has been chosen the definition of CC of Barrat (Barrat et al., 2004. As sparsity increases, CC tends to zero, while, trivially, CC = 1 in a fully connected graph. It should be noted, however, that the transitivity index does not have a linear relation with network sparsity, instead it emphasizes the propensity of a network to form clusters (Saramäki et al., 2007), i.e., groups of densely connected nodes, as commonly found in real-world social networks.
Global Efficiency
Related to the degree of proximity between nodes, the Average Shortest Path Length (ASPL) or its inverse measure, the Global Efficiency (GE ), refers to the average number of edges required to connect each node with all othernodes (Newman, 2001; Mao & Zhang, 2013). Consequently, GE provides a measure of the average connectivity between the nodes within the network. As in the case of the Global Transitivity metric, there are several methods for computing the ASPL, including calculation methods for weighted networks, such as the Dijkstra's algorithm (Newman, 2001; Dijkstra, 2022). In Dijkstra's algorithm, the weighted path connecting to nodes is provided by the summation of the inverse of the edge’s weights; and in minimizing such summation we assign higher probability to paths connecting greater values (correlations), seemingly to resistors in parallel in an electric circuit.
Small-Worldness Index
A last metric, which became very popular in recent years due to its applications in real world networks, is the Small-Worldness Index (Humphries & Gurney, 2008). This composite metric, calculated as the ratio of the Global Transitivity Index (CC ) over ASPL, refers to the tendency of the network to have a high clustering degree and a moderate connectivity degree between nodes (Watts, 1999; Watts & Strogatz, 1998; Borsboom et al., 2011; Watts, 2016).