Synergistic Graph Fusion via Encoder Embedding

This information can be captured by an n n adjacency matrix A, where A(i, j) = 1 indicates the existence of an edge between vertices i and j, and A(i, j) = 0 indicates the absence of an edge. Traditionally, the adjacency matrix is binary and primarily used for representing unweighted graphs. Its capacity extends to handling weighted graphs, where the elements of A are assigned the corresponding edge weights. Moreover, graph representation can be used for any data via proper transformations. For instance, when vertex attributes are available, they can be transformed into a pairwise distance or kernel matrix, thus creating a general graph structure. This adaptability enables the incorporation of additional information from vertex attributes, making graph representation a powerful tool for data analysis that goes beyond traditional binary or weighted graphs. Graph embedding is a fundamental and versatile approach for analyzing and exploring graph data, encompassing a wide range of techniques such as spectral embedding [7, 8], graph convolutional neural networks [9, 10], node2vec [11, 12], among others. By projecting the vertices into a low-dimensional space while preserving the structural information of the graph, graph embedding yields vertex representations in Euclidean space that facilitate various downstream inference tasks, such as community detection [13, 14], vertex classification [15, 9], outlier detection [16, 17], etc.