Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detection

Typically, a graph (or network) is represented by an adjacency matrix A of size, where A(,) denotes the edge weight between the th and th vertices. Alternatively, the graph can be stored in an edgelist E of size 3, with the first two columns indicating the vertex indices of each edge and the last column representing the edge weight. Community detection, also known as vertex clustering or graph partitioning, is a fundamental problem in graph analysis [6, 8, 10, 13]. The primary objective is to identify natural groups of vertices where intra-group connections are stronger than inter-group connections. Over the years, various approaches have been proposed, including modularitybased methods [2, 22], spectral-based methods [15, 21], and likelihood-based techniques [1, 7], among others.