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# NautyGraphs : Table of Contents

- NautyGraphs -- Interface to nauty (Graphs fork)
- addEdges -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways
- areIsomorphic -- determines whether two graphs are isomorphic
- buildGraphFilter -- creates the appropriate filter string for use with filterGraphs and countGraphs
- Comparison of Graph6 and Sparse6 formats
- countGraphs -- counts the number of graphs in the list with given properties
- Example: Checking for isomorphic graphs
- Example: Generating and filtering graphs
- filterGraphs -- filters (i.e., selects) graphs in a list for given properties
- generateBipartiteGraphs -- generates the bipartite graphs with a given bipartition
- generateGraphs -- generates the graphs on a given number of vertices
- generateRandomGraphs -- generates random graphs on a given number of vertices
- generateRandomRegularGraphs -- generates random regular graphs on a given number of vertices
- graph6ToSparse6 -- converts a Graph6 string to a Sparse6 string
- graphComplement -- computes the complement of a graph
- graphToString -- converts a graph to a string in the Graph6 format
- isPlanar -- determines if a given graph is planar
- neighborhoodComplements -- complements the neighborhood for each vertex, individually
- newEdges -- replaces disjoint pairs of edges by disjoint pairs of two-chains
- onlyPlanar -- removes non-planar graphs from a list
- relabelBipartite -- relabels a bipartite graph so all vertices of a given class are contiguous
- relabelGraph -- applies a vertex invariant based refinement to a graph
- removeEdges -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways
- removeIsomorphs -- removes all isomorphs from a list of graphs
- sparse6ToGraph6 -- converts a Sparse6 string to a Graph6 string
- stringToEdgeIdeal -- converts a Sparse6 or Graph6 String to an edge ideal in the given polynomial ring
- stringToGraph -- converts a Sparse6 or Graph6 String to a Graph