Spectral Theory
An adjacency matrix is a square matrix used to represent a finite graph, where the elements indicate whether pairs of vertices are adjacent or not in the graph. Each row and column corresponds to a vertex, and if there is an edge connecting two vertices, the corresponding element in the matrix is marked with a 1 (or the weight of the edge if it’s weighted), while a 0 indicates no edge. This representation is crucial in understanding various properties of graphs, especially in relation to concepts like graph Laplacians and eigenvalues.
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