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A drawing of a graph with 6 vertices and 7 edges.. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Hence any standard graph theoretic concept that is independent of the edge orders | | will generalize to hypergraph theory. An undirected hypergraph ( X , E ) {\displaystyle (X,E)} is an undirected graph whose edges connect not just two vertices, but an arbitrary number. [ 2 ]
Contracting an edge without creating multiple edges. As defined below, an edge contraction operation may result in a graph with multiple edges even if the original graph was a simple graph. [2] However, some authors [3] disallow the creation of multiple edges, so that edge contractions performed on simple graphs always produce simple graphs.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A directed graph is weakly connected (or just connected [9]) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. A directed graph is strongly connected or strong if it contains a directed path from x to y (and from y to x) for every pair of vertices (x, y).
In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. [ 1 ] Formally, given a graph G = ( V , E ) , a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph .
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 ...
A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops. In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges [1]), that is, edges that have the same end nodes.
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