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Graph Properties

The following listing contains the more important functions that yield properties of a graph:

Graph Structure |
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GraphNumberOfEdges GraphNumberOfVertices |
edge or vertex count | |

GraphEdgeValuesMatrix GraphEdgeValuesList |
edge weights as matrix or as list | |

GraphAdjacencyMatrix GraphAdjacencyList |
adjacency matrix or list | |

GraphVerticesNeighbors | predecessors and successors for vertices | |

GraphUndirectedQ | test if graph is completely undirected | |

GraphStronglyCompleteQ GraphWeaklyCompleteQ |
test if all vertex pairs are connected by an edge |

Vertex Information |
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VertexDegree GraphDegrees |
vertex degree(s) in a graph | |

VertexIn/OutDegree GraphIn/OutDegrees |
in-degree(s) and out-degree(s) in a directed graph | |

GraphVerticesWithOddInDegree GraphVerticesWithOddOutDegree |
vertices with odd in-degree or out-degree | |

VertexIsolatedQ | test if vertex is not connected to an edge |

Edge Information |
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GraphNegativeEdgesQ | test if any edge has a negative weight | |

GraphParallelEdgesQ | test if graph contains parallel edges | |

GraphSelfLoopsQ | test if any vertex connects itself |

Path Properties |
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WalkLength | length of a path with respect to edge weights | |

WalkClosedQ | test if start and end vertex coincide | |

WalkCyclesQ | test if path contains any cycles |

Cycles and Trees |
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GraphCyclesQ | test if graph contains (undirected) cycles | |

GraphDirectedCyclesQ | test if graph contains directed cycles | |

GraphNegativeCyclesQ | test if graph contains any cycles with a negative length | |

GraphNegativeDirectedCyclesQ | test if graph contains any directed cycles with a negative length | |

GraphTreeQ | test if graph is a tree | |

GraphDirectedTreeQ | test if graph is a directed root tree |

Order |
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GraphTopologicalVertexOrderQ | test if graph is sorted topologically | |

AnyTopologicalVertexOrder | topologically sorted list of vertices |

Connectivity |
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GraphWeaklyConnectedQ | test if all vertices are connected by undirected edges | |

GraphStronglyConnectedQ | test if all vertices are connected by directed edges | |

GraphWeaklyConnectedComponentSet VertexWeaklyConnectedComponent |
vertex set(s) that are each weakly connected | |

GraphStronglyConnectedComponentSet VertexDirectedPathsToVertexSet VertexDirectedPathsFromVertexSet |
vertex set(s) that are each connected by directed edges | |

VertexPairWeaklyConnectedQ | test if two vertices are connected by undirected edges | |

VertexPairDirectedPathFromToQ | test if two vertices are connected by directed edges | |

VertexDirectedPathsToAllQ | test if a vertex can reach all others by directed edges | |

VertexDirectedPathsFromAllQ | test if a vertex can be reached from all others by directed edges |

Editorial/Data Protection • page checked on Nov. 28th 2005