Table 2 The network measures employed to characterize the IPs

1) Degree centrality

It expresses the number of links of a given node. It directly affects the capacity of a node to immediately influence the information flow in the network (Wasserman and Faust 1994).

2) Betweenness

It measures how often a given node is between two other nodes along their shortest path, that is how many times a node acts as a bridge. This measure can be interpreted as an indicator of how the single node plays the role of “gatekeeping” (Borgatti et al. 2013).

3) Closeness

It is the reciprocal of the farness of a node. It is expressed formally as the inverse of the sum of the distances from a certain node to all others in the network. The measure here used is a normalized version where the reciprocal of farness is expressed as a percentage of the minimum possible farness (Wasserman and Faust 1994).

4) Average reciprocal distance (ARD)

It measures how the node is close to the whole network. For a given node, it is calculated as the summation of all other nodes weighted for the reciprocal of the farness from the given node. The greater the value of this indicator, the greater is the “connectedness” of the node (Borgatti et al. 2013).

5) Local clustering coefficient

It is the density of the neighborhood of the given node. It ranges between 0 (any neighbor is connected with another) and 1 (the neighbors are fully connected) (Newman 2003).

6) Eigenvector

It looks at how close is the node with respect to the whole network, putting less importance on more “local” closeness.

It is calculated by means of a factor that identifies dimensions of the distances among actors. The first dimension identifies the “global” aspects of distances among actors, while the other dimensions capture more specific features (Hanneman and Riddle 2005).