This is an adapted version of the Glasgow Subgraph solver used for the subgraph isomorphism problem. This software is adapted to handle multiplex multichannel graphs as well as incorporate structural equivalence-inspired ideas for acceleration of solve time and better understanding of the solution space.

These adaptations were made by Dominic Yang, Jacob Moorman, and Denali Molitor at University of California, Los Angeles. The original solver on which these adaptations are built was based on papers by Blair Archibald, Ciaran McCreesh, Patrick Prosser and James Trimble at the University of Glasgow, Fraser Dunlop and Ruth Hoffman at the University of St Andrews. The original solver can be found at this Github page.

Any questions about this software should be referred to Dominic Yang

Subgraph Isomorphism is the task of finding a copy of a small pattern graph within a larger target graph. We wish to assign every pattern vertex to an associated target vertex while ensuring that the target vertices have the same neighborhood structure apparent in the pattern. For example, the mapping (A->1, B->2, C->3) is such a mapping but (A->1, B->2, C->6) is not because 6 is not adjacent to 1 while C is adjacent to A. We wish to accelerate the state-of-the-art solver Glasgow by incorporating structural equivalence into the algorithm.

Structural Equivalence, in the simplest terms, is the property of vertices of a graph having the exact same neighborhood. For example, in the above figure, vertices B and C would be structurally equivalent for they share the same neighbor, namely A. It is under these circumstances, that we can interchange pattern vertex assignments in any subgraph isomorphism to produce a new one.

We can go further by acknowledging, that in many circumstances, certain edges are effectively irrelevant to subgraph search, and obscure structural equivalence. To explain what we mean by this, consider mapping vertex A to vertex 1. In order to ensure a subgraph isomorphism, we need only assign B and C to any vertex adjacent to 1; any edges between the neighbors only obscures the similarity and are thus irrelevant. The task of determining relevancy is difficult and will be expounded upon in an associated paper to this package.

Compilation of the solver can be done with the make command. This requires a C++17 compiler as well as Boost to be installed.

To run the basic implementation to find a single isomorphism for pattern graph stored in pattern-file in a target graph stored in target-file

$ ./glasgow_subgraph_solver pattern-file target-file

There are a wide variety of options which can be found by executing

$ ./glasgow_subgraph_solver --help

We list some commonly used options:

1. --induced: Restrict algorithm to only find induced isomorphisms.
2. --count-solutions: Count all solutions, instead of stopping at the first found solution.
3. --print-all-solutions: Print all solutions found, if equivalence is used this will only print representative solutions.
4. --pattern-equivalence: One of none, structural, indicates equivalence level on pattern.
5. --target-equivalence: One of none, structural, candidate, full, or node_cover, indicates equivalence level on target.
6. --format: Indicate the format used for the graph files.

The solver currently only supports both pattern equivalence and target equivalence simultaneously if both are set to structural.

The file format which is currently supported by this library for multiplex graph processing is the csv format. This format is given by listing each edge in comma-separated format as three fields: the name of the first node, the name of the second node, and the edge label. If the edge is to be directed, the first comma is to be replaced by a > symbol. In order to support multigraphs, each edge is repeated according to its multiplicity. To include node labels, you can put the node name in the first field, leave the second field blank, and put the node label in the third field.

The following snippet adapted from the original Glasgow solver repository, demonstrates how to write in this format.

first>second,red
first>second,red
second>first,blue
first,third,purple
first>first,green
first,,circle
second,,circle
third,,square
fourth,,square