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An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...
An edge list is a data structure used to represent a graph as a list of its edges. An (unweighted) edge is defined by its start and end vertex, so each edge may be represented by two numbers. [1] The entire edge list may be represented as a two-column matrix. [2] [3] An edge list may be considered a variation on an adjacency list which is ...
The doubly connected edge list (DCEL), also known as half-edge data structure, is a data structure to represent an embedding of a planar graph in the plane, and polytopes in 3D. This data structure provides efficient manipulation of the topological information associated with the objects in question (vertices, edges, faces).
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 ...
For a simple graph with vertex set U = {u 1, …, u n}, the adjacency matrix is a square n × n matrix A such that its element A ij is 1 when there is an edge from vertex u i to vertex u j, and 0 when there is no edge. [1]
A synonym for an undirected edge. The line graph L(G) of a graph G is a graph with a vertex for each edge of G and an edge for each pair of edges that share an endpoint in G. linkage A synonym for degeneracy. list 1. An adjacency list is a computer representation of graphs for use in graph algorithms. 2.
In the context of efficient representations of graphs, J. H. Muller defined a local structure or adjacency labeling scheme for a graph G in a given family F of graphs to be an assignment of an O(log n)-bit identifier to each vertex of G, together with an algorithm (that may depend on F but is independent of the individual graph G) that takes as input two vertex identifiers and determines ...
In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as the incidence graph of a hypergraph when it is 2-colored and it is indicated which color class corresponds to hypergraph vertices and which to hypergraph edges.