A graph with a certain property can often be built starting from another graph. They may be a subgraph of a larger graph, they can be incrementally modified by deleting or adding elements, or they can be built by combining multiple graphs using Boolean operations. The Wolfram Language provides an extensive collection of functions for producing new graphs from old.

Selecting Subgraphs

Subgraph — extract a subgraph containing vertices, edges, or combinations

NeighborhoodGraph — extract a subgraph up to some distance from a graph element

FindSpanningTree — find a tree that connects all vertices

Conversion of Graphs

UndirectedGraph — convert a directed graph to an undirected graph

DirectedGraph — convert an undirected graph to a directed graph

ReverseGraph  ▪  SimpleGraph  ▪  IndexGraph

Tagging of Graphs

EdgeTaggedGraph — generate a graph with tagged edges

IndexEdgeTaggedGraph  ▪  EdgeTags  ▪  EdgeTaggedGraphQ

Modifications of Graphs

VertexReplace — replace vertices using rules

VertexAdd  ▪  VertexDelete  ▪  VertexContract  ▪  EdgeAdd  ▪  EdgeDelete  ▪  EdgeContract

Operations on Graphs

BooleanGraph — Boolean combination of graphs

LineGraph — give the line graph where edges become vertices and vice versa

GraphPower — graph with all vertices adjacent that are n steps or fewer apart

DualPlanarGraph — dual of a planar graph

GraphIntersection  ▪  GraphUnion  ▪  GraphDifference  ▪  GraphDisjointUnion  ▪  GraphComplement  ▪  GraphProduct  ▪  GraphJoin  ▪  GraphSum

Reachability and Relation

TransitiveClosureGraph — give the transitive closure

TransitiveReductionGraph — give the transitive reduction

Control Flow Graphs

DominatorTreeGraph — give the tree of immediate dominators

DominatorVertexList — give immediate dominators for each vertex