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In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs.
Another problem related to reachability queries is in quickly recalculating changes to reachability relationships when some portion of the graph is changed. For example, this is a relevant concern to garbage collection which needs to balance the reclamation of memory (so that it may be reallocated) with the performance concerns of the running ...
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
Adjacency list; Adjacency matrix. Adjacency algebra – the algebra of polynomials in the adjacency matrix; Canadian traveller problem; Cliques and independent sets. Clique problem; Connected component; Cycle space; de Bruijn sequences; Degree diameter problem; Entanglement (graph measure) Erdős–Gyárfás conjecture; Eternal dominating set ...
The Laplacian matrix is the easiest to define for a simple graph but more common in applications for an edge-weighted graph, i.e., with weights on its edges — the entries of the graph adjacency matrix. Spectral graph theory relates properties of a graph to a spectrum, i.e., eigenvalues and eigenvectors of matrices associated with the graph ...
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.
From the handshaking lemma, a k-regular graph with odd k has an even number of vertices. A theorem by Nash-Williams says that every k ‑regular graph on 2k + 1 vertices has a Hamiltonian cycle. Let A be the adjacency matrix of a graph. Then the graph is regular if and only if = (, …,) is an eigenvector of A. [2]