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.
@cite_16: In this paper, we study crucial elements of a complex network, namely its nodes and connections, which play a key role in maintaining the network’s structure and function under unexpected structural perturbations of nodes and edges removal. Specifically, we want to identify vital nodes and edges whose failure (either random or intentional) will break the most number of connected triples (or triangles) in the network. This problem is extremely important, because connected triples form the foundation of strong connections in many real-world systems, such as mutual relationships in social networks, reliable data transmission in communication networks, and stable routing strategies in mobile networks. Disconnected triples, analog to broken mutual connections, can greatly affect the network’s structure and disrupt its normal function, which can further lead to the corruption of the entire system. The analysis of such crucial elements will shed light on key factors behind the resilience and robustness of many complex systems in practice. We formulate the analysis under multiple optimization problems and show their intractability. We next propose efficient approximation algorithms, namely, DAK-n and DAK-e , which guarantee an @math -approximate ratio (compared with the overall optimal solutions) while having the same time complexity as the best triangle counting and listing algorithm on power-law networks. This advantage makes our algorithms scale extremely well even for very large networks. In an application perspective, we perform comprehensive experiments on real social traces with millions of nodes and billions of edges. Empirical results indicate that our approaches achieve comparably better solution quality while are up to @math faster than the current state-of-the-art methods.
@cite_1: We introduce Community structure Vulnerability Assessment (CVA) problem to assess the network vulnerability under a community structure point of view. Given a positive number k, CVA aims to find out the k most vulnerable nodes whose removals maximally transform the current network community structure to a different one. As the first attempt, we suggest an approximation algorithm for the special case k = 1, and propose multiple greedy algorithms for CVA problem. To certify the effectiveness of suggested approaches, we test them on not only synthesized networks with known community structures but also on real-world social traces.
Assessing the structural network vulnerability has received increasing attention. For example, @cite_1 have proposed a Community Vulnerability Assessment (CVA) problem and suggested multiple heuristic based algorithms based on the modularity measure of communities in the network. These approaches are restricted to the scope of online social networks and do not cater to general network structures. Another work by @cite_16 explored the number of connected triplets in a network as they capture the strong connection of communities in social networks.