Graph Operations and Modifications

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 built by combining multiple graphs using Boolean operations.

*Mathematica* provides an extensive collection of functions for producing new graphs from old.

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

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

UndirectedGraph — convert a directed graph to an undirected graph

DirectedGraph — convert an undirected graph to a directed graph

VertexReplace — replace vertices using rules

BooleanGraph — Boolean combination of graphs

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

GraphPower — graph with all vertices adjacent that are

n steps or fewer apart