Using adjacency matrix representation will change the time of scanning through neighbours from O(E) to O(V²).
Therefore, total running time becomes O(V² + V), that is, O(V²).
An adjacency matrix, which is a square matrix used to represent a finite graph, is a tool in graph theory and computer science. If two sets of vertices in the graph are adjacent or not, it is indicated by the matrix's elements.
A (0,1)-matrix with zeros on its diagonal makes up the adjacency matrix in the special case of a finite simple graph. The adjacency matrix is symmetric if the graph is undirected, which means that every edge is directed in only one direction. In spectral graph theory, it is investigated how a graph's adjacency matrix's eigenvalues and eigenvectors relate to one another.
It is important to distinguish a graph's adjacency matrix from its degree matrix and incidence matrix, which both represent matrices differently and contain elements that indicate whether or not vertex-edge pairs are incident.
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