Novel Rewiring Mechanism for Restoration of the Fragmented Social Networks after Attacks

TL;DR

This research work delves deeper into evaluating the robustness of the restored network by evaluating Laplacian Energy to better comprehend the system's behavior during the restoration of the network still considering the size of the largest connected component attacks.

Abstract

Real-world complex systems exhibit intricate interconnections and dependencies, especially social networks, technological infrastructures, and communication networks. These networks are prone to disconnection due to random failures or external attacks on their components. Therefore, managing the security and resilience of such networks is a prime concern, particularly at the time of disaster. Therefore, in this research work, network is reconstructed by rewiring/addition of the edges and robustness of the networks is measured. To this aim, two approaches namely (i) Strategic rewiring (ii) budget constrained optimal rewiring are adopted. While current research often assesses robustness by examining the size of the largest connected component, this approach fails to capture the complete spectrum of vulnerability. The failure of a small number of connections leads to a sparser network yet connected network. Thus, the present research work delves deeper into evaluating the robustness of the restored network by evaluating Laplacian Energy to better comprehend the system's behavior during the restoration of the network still considering the size of the largest connected component attacks.

Figures (5)

• Figure 1: A toy network to illustrate the rewiring process.
• Figure 2: (a) Initially, the network is under attack and splits into six components. The nodes in the Largest Connected Component (LCC) are $[0,4,5,6,8,12,13,14,16,17,18]$, while the remaining five disconnected components consist of the following node lists:$[[19,10,2,11],[9,3,15],[1],[7]]$. (b) Since the number of edges in the LCC is less than 20 (the number of nodes), an edge is added between node 12 (the node with the maximum degree in the LCC) and node 10 (the node with the maximum degree in the component $[19,10,2,11]$). (c) With the addition of the new edge in the LCC, the number of edges is still less than 20, so another edge is added, this time between node 12 of the LCC and node 9. (d) Once the number of edges in the LCC reaches 20, rewiring takes place according to Algorithm \ref{['algo3']}, and node 7 is connected to node 12 in the LCC. (e) The rewiring process continues, and eventually, the entire network is restored.
• Figure 3: Left panel (a,c,e) represents the plot of parameters $L_{\mathcal{E}}$, $S$ and $\rho$ respectively for the random network having $n=500, p = 0.01$ and right panel (b,d,f) represent the same parameters for Power Law Network with $n=500, p=0.02$.
• Figure 4: Left panel (a,c,e) represents the plot of parameters $L_{\mathcal{E}}$, $S$ and density $\rho$ respectively for the Power Law Network having $n = 500, \gamma = 2.1$ and right panel (b,d,f) represent the same parameters for Power Law Network with $n=500, \gamma = 2.7$.
• Figure 5: The plot of parameters $L_{\mathcal{E}}$, $S$ and density $\rho$ respectively for the email university network having $n = 1133, m = 5154$.