isomorphism (biograph)

Find isomorphism between two biograph objects

Syntax

[Isomorphic, Map] = isomorphism(BGObj1, BGObj2)
[Isomorphic, Map] = isomorphism(BGObj1, BGObj2,'Directed', DirectedValue)

Arguments

BGObj1Biograph object created by biograph (object constructor).
BGObj2Biograph object created by biograph (object constructor).
DirectedValueProperty that indicates whether the graphs are directed or undirected. Enter false when both BGObj1 and BGObj2 produce undirected graphs. In this case, the upper triangles of the sparse matrices extracted from BGObj1 and BGObj2 are ignored. Default is true, meaning that both graphs are directed.

Description

[Isomorphic, Map] = isomorphism(BGObj1, BGObj2) returns logical 1 (true) in Isomorphic if two N-by-N adjacency matrices extracted from biograph objects BGObj1 and BGObj2 are isomorphic graphs, and logical 0 (false) otherwise. A graph isomorphism is a 1-to-1 mapping of the nodes in the graph from BGObj1 and the nodes in the graph from BGObj2 such that adjacencies are preserved. Return value Isomorphic is Boolean. When Isomorphic is true, Map is a row vector containing the node indices that map from BGObj2 to BGObj1. When Isomorphic is false, the worst-case time complexity is O(N!), where N is the number of nodes.

[Isomorphic, Map] = isomorphism(BGObj1, BGObj2,'Directed', DirectedValue) indicates whether the graphs are directed or undirected. Set DirectedValue to false when both BGObj1 and BGObj2 produce undirected graphs. In this case, the upper triangles of the sparse matrices extracted from BGObj1 and BGObj2 are ignored. The default is true, meaning that both graphs are directed.

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References

[1] Fortin, S. (1996). The Graph Isomorphism Problem. Technical Report, 96-20, Dept. of Computer Science, University of Alberta, Edomonton, Alberta, Canada.

[2] McKay, B.D. (1981). Practical Graph Isomorphism. Congressus Numerantium 30, 45-87.

[3] Siek, J.G., Lee, L-Q, and Lumsdaine, A. (2002). The Boost Graph Library User Guide and Reference Manual, (Upper Saddle River, NJ:Pearson Education).

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