org.metasyntactic.math
Interface UndirectedGraph

All Superinterfaces:

Graph

public interface UndirectedGraph

extends Graph

In an undirected graph G = (V, E), the edge set E consists of unordered pairs of vertices, rather then ordered pairs. ∈ V and u ≠ v. By convention, we use the notation (u, v) for an edge, rather than the set notation {u, v}, and (u, v) and (v, u) are considered to be the same edge. In an undirected graph, self-loops are forbidden, and so every edge consists of exactly two distinct vertices.

Nested Class Summary

Nested classes inherited from class org.metasyntactic.math.Graph

Graph.Edge, Graph.Path

Method Summary

boolean	isBipartite() A bipartite graph is an undirected graph G = (V, E) in which V can be partitioned into two sets V1 and V2 such that (u, v) ∈ E implies that either (u ∈ V1 and v ∈ V2) or (u ∈ V2 and v ∈ V1).
boolean	isComplete() A complete graph is an undirected graph in which every pair of vertices is adjacent.
boolean	isConnected() An undirected graph is connected if every pair of vertices is connected by a path.

Methods inherited from interface org.metasyntactic.math.Graph

addEdge, addVertex, areAdjacent, containsEdge, containsVertex, degree, getEdges, getVertices, induce, isReachable, isSubgraph

Method Detail

isComplete

public boolean isComplete()

A complete graph is an undirected graph in which every pair of vertices is adjacent.

Returns:

true If this undirected graph is complete

isBipartite

public boolean isBipartite()

A bipartite graph is an undirected graph G = (V, E) in which V can be partitioned into two sets V₁ and V₂ such that (u, v) ∈ E implies that either (u ∈ V₁ and v ∈ V₂) or (u ∈ V₂ and v ∈ V₁). That is, all edges go between the two sets V₁ and V₂.

isConnected

public boolean isConnected()

An undirected graph is connected if every pair of vertices is connected by a path.

Returns:

true if this undirected graph is connected