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SOLUTIONS
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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.
ReferenceReference
Selecting Subgraphs
Subgraph — extract a subgraph containing vertices, edges, or combinations
NeighborhoodGraph — extract a subgraph up to some distance from a graph element
Conversion of Graphs
UndirectedGraph — convert a directed graph to an undirected graph
DirectedGraph — convert an undirected graph to a directed graph
ReverseGraph ▪ SimpleGraph ▪ IndexGraph
Modifications of Graphs
VertexReplace — replace vertices using rules
VertexAdd ▪ VertexDelete ▪ EdgeAdd ▪ EdgeDelete
Operations on Graphs
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
GraphIntersection ▪ GraphUnion ▪ GraphDifference ▪ GraphDisjointUnion ▪ GraphComplement
