Graph connectivity

sequence of edges connecting a sequence of vertices in a graph, with no repeating vertices

maximal subgraph of a given node-link graph within which every two vertices may be connected by a path

subgraph of a directed graph containing paths in both directions between each pair of vertices

edge of a graph whose deletion increases the graph's number of connected components; equivalently, an edge not contained in any cycle

any measure of how connected a graph is

in graph theory, partition of the vertices in two sets

theorem characterizing graph connectivity by disjoint paths

graph theory algorithm

algorithm to find the strongly connected component of a directed graph

graph with more than k vertices that cannot be disconnected by the deletion of fewer than k vertices

randomized algorithm for minimum cuts

graph that remains connected whenever fewer than k edges are removed

In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s can reach a vertex t (and t is reachable from s) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with s and ends with t.

graph on at least 3 vertices that remains connected when any one vertex is removed

theorem in graph theory

mathematical theorem concerning the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes

notion in graph theory

matroid whose independent sets are forests in an undirected graph

second-smallest eigenvalue of a graph Laplacian

Recursive algorithm in graph theory

graph invariant

concept in graph theory, a branch of mathematics

graph connectivity property

thumb|300px|There is a path (graph theory)|path directed from "s" to "t" in the first graph, but not in the second.