Overlapping community detection algorithms using Modularity and the cosine

The issue of network community detection has been extensively studied across many fields. Most community detection methods assume that nodes belong to only one community. However, in many cases, nodes can belong to multiple communities simultaneously.This paper presents two overlapping network community detection algorithms that build on the two-step approach, using the extended modularity and cosine function. The applicability of our algorithms extends to both undirected and directed graph structures. To demonstrate the feasibility and effectiveness of these algorithms, we conducted experiments using real data.