Forecasting real-world complex networks’ robustness to node attack using network structure indexes - Bellingeri, Michele; Turchetto, Massimiliano; Scotognella, Francesco; Alfieri, Roberto; Nguyen, Ngoc-Kim-Khanh; Nguyen, Quang; Cassi, Davide (Frontiers in Physics, 2023)
Here, 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 in which 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 𝑞 𝑐 ', i.e., the fraction of nodes removed for which the size of the 𝐿𝐶𝐶 is quasi-zero. We correlate the 𝑞 𝑐 with 20 network structural indicators (NSI) 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 index (𝐸𝐻), evaluating the degree difference of connected nodes, best predicts the 𝑞 𝑐 . The Estrada heterogeneity index (𝐸𝐻) 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 𝑞 𝑐 decreases as a function of the 𝐸𝐻 index, unveiling that heterogeneous real-world networks with higher variance in the degree of connected nodes are more vulnerable to node attacks.