Optimizing Combined Centrality Measures in Complex Networks via Arithmetic Optimization and Representative Graphs

ABSTRACT Complex networks are prevalent in various real‐world domains, including social networks, biological networks, communication networks, and information networks. Identifying the significance of nodes within these networks provides numerous advantages, such as detecting influential individuals, identifying structurally similar nodes, and facilitating community analysis. However, due to the absence of a universally accepted definition of node importance, multiple centrality measures have been developed to quantify it. Each centrality measure evaluates node significance from a distinct perspective. By utilizing multiple measures in conjunction or integrating them, a more comprehensive understanding of node importance can be achieved. Combining multiple centrality measures into a linear combination involves determining a coefficient for each sub‐centrality measure, which can be computationally intensive. Additionally, developing separate combined measures for different graphs requires repeating this process for each case. This study proposes the use of the Arithmetic Optimization Algorithm (AOA) to determine these coefficients. It also suggests that generating a combined centrality measure from a synthetic Representative Graph, created by averaging the degree distributions of similar graphs, may produce effective results for the original graphs. Experimental results indicate that the AOA algorithm can quickly determine coefficients for combined centrality measures, and the Representative Graph method performs effectively.