| Graph Structure | ||
| 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 | ||
| 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 | ||
| 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 | ||
| 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 | ||
| 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 | ||
| GraphTopologicalVertexOrderQ | test if graph is sorted topologically | |
| AnyTopologicalVertexOrder | topologically sorted list of vertices |
| Connectivity | ||
| 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 |