Connected component (graph theory)

In graph theory, a connected component (or just component) of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph.

For example, the graph shown in the illustration on the right has three connected components.

A vertex with no incident edges is itself a connected component.

A graph that is itself connected has exactly one connected component, consisting of the whole graph.

See also

Biconnected component Bridge (graph theory) Centrality Connected-component labeling, a basic technique in computer image analysis based on connected components of graphs Giant component Modular decomposition, for a proper generalization of connected components on undirected graphs Strongly connected component, a related concept for directed graphs Percolation theory, a theory describing the behavior of connected components in random subgraphs of grid graphs Centrality

External links

• Connected component (graph theory) @ Wikipedia