Editorial/Data Protection
Graph Properties
The following listing contains the more important functions that yield properties of a graph:

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