Otherwise, it is called a weakly connected graph if every ordered pair of vertices in the graph is weakly connected. Otherwise, the ordered pair is called disconnected.Ī strongly connected graph is a directed graph in which every ordered pair of vertices in the graph is strongly connected. Otherwise, the ordered pair is called weakly connected if an undirected path leads from x to y after replacing all of its directed edges with undirected edges. In a directed graph, an ordered pair of vertices ( x, y) is called strongly connected if a directed path leads from x to y. Otherwise, it is called a disconnected graph. Otherwise, the unordered pair is called disconnected.Ī connected graph is an undirected graph in which every unordered pair of vertices in the graph is connected. The vertices x and y of an edge is called connected if a path leads from x to y. Ī graph with three vertices and three edges.Ī graph (sometimes called undirected graph for distinguishing from a directed graph, or simple graph for distinguishing from a multigraph) is a pair G = ( V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of paired vertices, whose elements are called edges (sometimes links or lines). Sylvester in 1878 in a direct relation between mathematics and chemical structure (what he called chemico-graphical image). The word "graph" was first used in this sense by J. Graphs are the basic subject studied by graph theory. The former type of graph is called an undirected graph while the latter type of graph is called a directed graph. In contrast, if any edge from a person A to a person B corresponds to A owes money to B, then this graph is directed, because owing money is not necessarily reciprocated. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with a person B only if B also shakes hands with A. Graphs are one of the objects of study in discrete mathematics. Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". A graph with six vertices and seven edges.
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