Forecasting real-world complex networks’ robustness to node attack using network structure indexes

In this study, we simulate the degree and betweenness node attack over a large set of 200 real-world networks from different areas of science. We perform an initial node attack approach, where the node centrality rank is computed at the beginning of the simulation, and it is not updated along the node removal process. We quantify the network damage by tracing the largest connected component (LCC ) and evaluate the network robustness with the “percolation threshold qc ,” i.e., the fraction of nodes removed, for which the size of the LCC is quasi-zero. We correlate qc with 20 network structural indicators (NSIs) from the literature using single linear regression (SLR), multiple linear regression (MLR) models, and the Pearson correlation coefficient test. The NSIs cover most of the essential structural features proposed in network science to describe real-world networks. We find that the Estrada heterogeneity (EH ) index, evaluating the degree difference of connected nodes, best predicts qc . The EH index measures the network node degree heterogeneity based on the difference of functions of node degrees for all pairs of linked nodes. We find that the qc value decreases as a function of the EH index, unveiling that heterogeneous real-world networks with a higher variance in the degree of connected nodes are more vulnerable to node attacks.