Connected graph

A graph in which every pair of vertices is joined by a path. In a directed graph, connectivity depends on whether paths must respect edge directions.

Graph (discrete mathematics): A structure consisting of vertices and edges that connect pairs of vertices. Connectedness is a property defined for graphs.
Depth-first search: A graph traversal that explores each branch as far as possible before backtracking. A single traversal can check whether every vertex is reachable from a chosen start.
Strongly connected component: A maximal set of vertices in a directed graph, each reachable from every other in both directions. Directed connectivity requires paths in both directions, unlike ordinary undirected connectivity.
Network topology: The arrangement of nodes and links in a communication or computer network. A network's graph is connected when every node can communicate through links, subject to direction and operation.
Path (graph theory): A sequence of vertices in which consecutive vertices are joined by edges. A path is the route that must exist between every vertex pair.
Breadth-first search: A graph traversal that visits vertices in increasing distance from a starting vertex. It tests reachability while also finding shortest paths in unweighted graphs.
Weakly connected component: A connected component formed by ignoring the directions of a directed graph's edges. It can classify a directed graph as connected even when directed paths fail.
Reliability engineering: The discipline of designing systems to function reliably under specified conditions. Connectivity helps quantify whether a network remains functional after component failures.
Vertex (graph theory): An element of a graph representing an object or position. Connectedness asks whether every pair of vertices can be linked.
Bridge (graph theory): An edge whose removal increases the number of connected components of a graph. A bridge is an edge whose loss destroys connectivity between some vertices.

Linked from 11 pages