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Graph Representation and Properties
Graphs are first-class citizens in Mathematica, and can be used as input, output, in programs, and in documents. Undirected and directed graphs are treated uniformly and support a number of standard properties for vertices and edges. Importantly, graphs also support custom properties for modeling or computational flexibility. Graphs can be converted to a number of different representations, including matrices. Graphs can be exported with high-fidelity to numerous file formats.
Reference
Graph — represent a general graph, or create it from vertices and edges
UndirectedEdge — an undirected edge (
)
DirectedEdge — a directed edge (
)
GraphQ ▪ UndirectedGraphQ ▪ DirectedGraphQ ▪ EdgeQ ▪ VertexQ
Basic Properties
VertexCount, EdgeCount — the number of vertices and edges in the graph
VertexList, EdgeList — the list of vertices and edges in the graph
VertexIndex, EdgeIndex — the index for a vertex or edge in a graph
EdgeRules — the list of edges as a list of rules
Standard Properties
EdgeShapeFunction, EdgeStyle, EdgeLabels — render, style, and label edges
VertexShapeFunction, VertexStyle, VertexLabels — render, style, and label vertices
GraphLayout, GraphStyle, GraphHighlightStyle — layout, style, and highlight graphs
EdgeWeight ▪ EdgeCapacity ▪ VertexShape ▪ VertexWeight ▪ VertexCapacity ▪ VertexCoordinates ▪ VertexSize ▪ GraphHighlight
Custom Properties »
Property — property wrapper for vertices and edges
PropertyValue — get and set vertex or edge property values
PropertyList ▪ SetProperty ▪ RemoveProperty ▪ Properties
Matrix Representations »
AdjacencyMatrix — vertex-vertex adjacency matrix
IncidenceMatrix ▪ KirchhoffMatrix ▪ WeightedAdjacencyMatrix ▪ ...
Exporting Graphs »
Export — export graphs into several graph formats
"GraphML" ▪ "GXL" ▪ "Graphlet" ▪ "Pajek" ▪ "TGF" ▪ "DOT" ▪ "DIMACS" ▪ "Graph6" ▪ "Sparse6" ▪ "LEDA"
