Stratified communities in complex business networks

In this work, we propose a measure that aims at assessing the position of a node with respect to the interconnected groups of nodes existing in a network. In particular, since the nodes of a network can be placed at different distances from cohesive groups, we extend the standard concept of clustering coefficient and provide the local l-adjacency clustering coefficient of a node i as an opportunely weighted mean of the clustering coefficients of nodes which are at distance l from i. Thus, the standard clustering coefficient is a peculiar local l-adjacency clustering coefficient for l = 0. As l varies, the local l-adjacency clustering coefficient is then used to infer insights on the position of each node in the overall structure. Empirical experiments on special business networks are carried out. In particular, the analysis of air traffic networks validate the theoretical proposal and provide supporting arguments on its usefulness.