Discovering Communities in Networks: A Linear Programming Approach Using Max-Min Modularity

Abstract

Community detection is a fundamental challenge in network science and graph theory that aims to reveal nodes' structures. While most methods consider Modularity as a community quality measure, Max-Min Modularity improves the accuracy of the measure by penalizing the Modularity quantity when unrelated nodes are in the same community. In this paper, we propose a community detection approach based on linear programming using Max-Min Modularity. The experimental results show that our algorithm has a better performance than the previously known algorithms on some well-known instances.

An Integer Programming Approach Reinforced by a Message-passing Procedure for Detecting Dense Attributed Subgraphs

“…Nevertheless, as discussed, Max-Min Modularity itself suffers from a critical issue: the nonexistence of a systematic way for proposing the so-called relation matrix, which is required to express the relationship between nonadjacent nodes. In this respect, Ferdowsi and Khanteymoori [16] succeeded in offering an analytical procedure to address this deficiency, generalize the conventional Max-Min Modularity, and provide an efficient local search-based algorithm to discover high-quality communities by considering both existing and missing links.…”

“…For the first task, we use the row/column generation algorithm proposed in [16] that perfectly works for (LP-MM) as well since the two models are identical apart from using different relation matrices. A summary of the applied row/column generation technique is as follows.…”

“…As a crucial remark, we can note that not only is the Max-Min Modularity Maximization problem categorized in the class of NP-hard problems [15], making it hard to find an efficient optimization algorithm, but it also suffers from a major drawback: Max-Min Modularity strongly depends on the accuracy of the given relation matrix, meaning that the quantity of the measure might be heavily affected by the node relationships defined by the user/oracle in the first place. De-spite Ferdowsi and Khanteymoori [16] succeeded in proposing a systematic approach for unveiling the relation between nonadjacent vertices, from a more critical point of view, one could argue that both Modularity and Max-Min Modularity, like many other community discovery methods, only utilize topological information of nodes, naively overlooking a rich set of nodal attributes (e.g., user profiles of an online social network or textual contents of a citation network), which is abundant in all real-life networks [17].…”

Toward unraveling multi-objective optimization problems: A hybrid approach for solving a novel facility location problem

“…The privilege of genetic algorithms is that a single run of the optimization algorithm is often needed to develop a Pareto curve because these methods use a population of possible solutions rather than a single search agent. Nevertheless, it is worth mentioning that the nature of the context problem can also have a severe impact on choosing/obtaining a proper optimization technique [23]. From this perspective, we converge our focus on one of the well-known and crucial optimization problems: the Facility Location Problem.…”

TSCDA: A novel greedy approach for community discovery in networks

“…Edge inside [47] |E in C | Average degree [47] [21] |i∈C,|(i,j)∈E:j∈C|<deg(u)/2| |C| sults, they usually fail to encounter extensive networks since optimizing the quality functions often falls into the category of difficult computational problems [50]. Therefore, in most cases, a heuristic method need to be inevitably employed to increase the (time) efficiency [20]. Accordingly,while dealing with massive networks, which we usually face in the real world, one acceptable approach would be to rely on heuristic techniques from the very beginning [12].…”