Many algorithms and procedures require graphs with certain properties. These can be basic properties, such as being undirected, or deeper topology properties, such as being connected or acyclic. In some areas, a key problem is to decide whether two graphs are the same if the vertex names are replaced, i.e. to test whether they are isomorphic.

Basic Properties

GraphQ — test whether an expression is a graph object

EdgeQ — test whether an expression is an edge in a graph

VertexQ — test whether an expression is a vertex in a graph

Local Structural Properties

EmptyGraphQ  ▪  UndirectedGraphQ  ▪  DirectedGraphQ  ▪  LoopFreeGraphQ  ▪  SimpleGraphQ  ▪  WeightedGraphQ

Global Structural Properties

IsomorphicGraphQ — test whether two graphs are the same after vertex renaming

FindGraphIsomorphism — find the graph isomorphism as a list of rules

AcyclicGraphQ  ▪  BipartiteGraphQ  ▪  ConnectedGraphQ  ▪  EulerianGraphQ  ▪  HamiltonianGraphQ  ▪  PathGraphQ  ▪  PlanarGraphQ  ▪  TreeGraphQ