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.

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<p>The focus of this paper is to provide an authentic approach to solving bi-objective optimization problems. The target problem is a novel extension of a multi-period $p$-mobile hub location problem, which takes into account the impact of the traveling time at the hubs' network, the time spent at each hub for processing the flows, and the delay caused by congestion at hubs with specific capacities. We first develop a mixed-integer mathematical model corresponding to the context problem. Afterward, a hybrid meta-heuristic algorithm will be proposed to solve the unveiled model that operates based on simultaneously employing a novel evaluation procedure, a clustering technique, and a genetic approach. The experiments validate that the proposed algorithm performs significantly better than several state-of-the-art algorithms. Furthermore, the decisive effect of two considerable factors: congestion and service time, are also analyzed.</p>

One of the recent challenging but vital tasks in graph theory and network analysis, especially when dealing with graphs equipped with a set of nodal attributes, is to discover subgraphs consisting of highly interacting nodes with respect to the number of edges and the attributes' similarities. This paper proposes an approach based on integer programming modeling and the graph neural network message-passing manner for efficiently extracting these subgraphs. The experiments illustrate the proposed method's privilege over some alternative algorithms known so far, utilizing several well-known instances.

In this paper, we introduce a new approach for detecting community structures in networks. The approach is subject to modifying one of the connectivity-based community quality functions based on considering the impact that each community's most influential node has on the other vertices. Utilizing the proposed quality measure, we devise an algorithm that aims to detect high-quality communities of a given network based on two stages: finding a promising initial solution using greedy methods and then refining the solutions in a local search manner. The performance of our algorithm has been evaluated on some standard real-world networks as well as on some artificial networks. The experimental results of the algorithm are reported and compared with several state-of-the-art algorithms. The experiments show that our approach is competitive with the other well-known techniques in the literature and even outperforms them. This approach can be used as a new community detection method in network analysis.