# Understanding Vulnerability of Communities in Complex Networks

## TL;DR

This paper investigates the vulnerability of community structures in complex networks by identifying critical nodes whose removal significantly alters the network's community organization, proposing scalable heuristics for large-scale analysis.

## Contribution

It introduces novel heuristics for identifying vital nodes affecting community structure, scalable to large networks, and demonstrates their effectiveness in network analysis and information diffusion tasks.

## Key findings

- Heuristics effectively identify critical nodes in small and large networks.
- Proposed methods improve community robustness analysis.
- Algorithms enhance information diffusion control.

## Abstract

In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural perturbations. Specifically, we want to identify all vital nodes, which when removed would lead to a large change in the underlying community structure of the network. This problem is extremely important because the community structure of a network allows deep underlying insights into how function of a network and its topology affect each other. Moreover, it even provides a way to condense large graphs into smaller graphs where each community acts as a meta node and hence aids in easier network analysis. If this community structure was to be compromised by either accidental or intentional perturbations to the network, that would make such analysis difficult. Since the problem of identifying such vital nodes is computationally intractable, we propose some heuristics that allow us to find solutions close to the optimal solution. To certify the effectiveness of our approach, we first test these heuristics on small networks, and then move to larger networks to show that we achieve similar results. The results reveal that the proposed approaches are effective to analyze the vulnerability of communities in graphs irrespective of their size and scale. From the application point of view, we show that the proposed algorithm is scalable and can be applied to the information diffusion task to curtail the spread of active nodes which was observed empirically. Additionally, we show the performance of our algorithm through an extrinsic evaluation -- we employ two tasks, like prediction and information diffusion, and show that the effect of our algorithm on these tasks is higher than the other baselines.