Abstract
Real-world complex systems are often modeled by networks such that the elements are represented by vertices and their interactions are represented by edges. An important characteristic of these networks is that they contain clusters of vertices densely linked amongst themselves and more sparsely connected to nodes outside the cluster. Community detection in networks has become an emerging area of investigation in recent years, but most papers aim to solve single-objective formulations, often focused on optimizing structural metrics, including the modularity measure. However, several studies have highlighted that considering modularityas a unique objective often involves resolution limit and imbalance inconveniences. This paper opens a new avenue of research in the study of multi-objective variants of the classical community detection problem by applying multi-objective evolutionary algorithms that simultaneously optimize different objectives. In particular, they analyzed two multi-objective variants involving not only modularity but also the conductance metric and the imbalance in the number of nodes of the communities. With this aim, a new Pareto-based multi-objective evolutionary algorithm is presented that includes advanced initialization strategies and search operators. The results obtained when solving large-scale networks representing real-life power systems show the good performance of these methods and demonstrate that it is possible to obtain a balanced number of nodes in the clusters formed while also having high modularity and conductance values.
Highlights
Graph theory is one of the most important branches of mathematics
This paper proposes a new MOEA, called Multi-objective Generational Genetic Algorithm+ (MOGGA+), which extends the features of the Generational Genetic Algorithm+ (GGA+) [6] that has successfully been applied to the classical single-objective formulation of the community detection problem
This paper proposes the analysis of two bi-objective formulations of the community detection problem based on some previous studies that have highlighted that most papers related to community detection aim to optimize structural metrics such as modularity and conductance while ignoring an important dimension: community size [38]
Summary
Graph theory is one of the most important branches of mathematics. Graphs are often used to model networks such that nodes (vertices) are the elements and links (edges) denote interactions between these elements. Graph theory is used to model real-life complex systems using graphs and to understand the role of the nodes within a given network. Some applications of graph theory are found in the study of transportation networks, computer and interconnection networks, telecommunication networks, electrical networks, biological systems, social networks, etc. Community detection is an emerging area of research that is attracting interest among scientists studying complex networks. The aim here is to detect community structures, that is, groups of densely
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