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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 ) .
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).
Similarly for a directed trail or a path. If there is a finite directed walk between two distinct vertices then there is also a finite directed trail and a finite directed path between them. A "simple directed path" is a path where all vertices are distinct. A weighted directed graph associates a value (weight) with
A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example, if a graph represents a road network, the weights could represent the length of each road.
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
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 computer science terms, a property graph is a data structure representing entities associated by directed relationships, where the nodes and relations can both include multiple attributes / properties; In terms of graph theory, a property graph is a directed multigraph, whose vertices/nodes represent the entities of the corresponding data ...
A vertex-weighted graph has weights on its vertices and an edge-weighted graph has weights on its edges. well-colored A well-colored graph is a graph all of whose greedy colorings use the same number of colors. well-covered A well-covered graph is a graph all of whose maximal independent sets are the same size. wheel