Library to resolve Maximal Cliques in undirected graph


Keywords
Algorithm, Maximal Cliques, complete graph, undirected graph, Bron Kerbosch
License
GPL-3.0-only

Documentation

MaximalCliques

PHP Library to resolve Maximal Cliques in undirected graph

A clique of a graph G is a complete subgraph of G. A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique

This implementation of Bron–Kerbosch's algorithm include three methods:

  • Basic resolution (obtainCompleteGraphsWithoutPivoting)
  • Pivoting resolution (obtainCompleteGraphsWithPivoting)
  • Vertex ordering resolution (obtainCompleteGraphsWithVertexOrdering)

And three methods based on "obtainCompleteGraphsWithVertexOrdering" for advancing search and less time of resolution:

  • Only cliques that include a specific vertex (obtainCompleteGraphsWithVertexOrderingForVertex)
  • Only cliques whose degree is equal to or greater than the specified (obtainCompleteGraphsWithVertexOrderingWithMinimumDegree)
  • Only cliques that include a specific vertex and whose degree is equal to or greater than the specified (obtainCompleteGraphsWithVertexOrderingForVertexWithMinimumDegree)

Finally, a function is included to collect the clique larger than those generated with one of the previous six functions.

  • (retrieveMaximalClique)

The six implementations return a array of maximal cliques each represented in an array of vertex, "retrieveMaximalClique" returns a array of vertex.

For a graph G whit 6 nodes:

6 - 4 - 5 - 1
    |   |  /
    |   | /
    |   |/
    3 - 2

This will be composed of five maximal cliques:

[
    [1,2,5],
    [2,3],
    [3,4],
    [4,5],
    [4,6]
]

Installation

for php 5.3 or lower use:
composer require "skilla/maximal-cliques:0.1.*"

for php 5.4 or higher
composer require "skilla/maximal-cliques:dev-master"

How to use

The source code includes "DataTransformerExample" class that implements the "DataTransformerInterface" interface. The purpose of this is to serve as a test and example.
Copy this class and adapt their methods to be able to process the data as generated in your application.
Then follow any of the examples used to test the class in "test / BronKerboschAlgorithmsTest.php"

Performance

Test 1 - 1,000 repetitions with the function "obtainCompleteGraphsWithoutPivoting". Using the same data as in the test.
Vertex: 6
Edges: 7
Cliques: 5
Time: 0.347 seconds
Memory: 786,432 bytes

Test 2 - 1,000 repetitions with the function "obtainCompleteGraphsWithPivoting". Using the same data as in the test.
Vertex: 6
Edges: 7
Cliques: 5
Time: 0.480 seconds
Memory: 786,432 bytes

Test 3 - 1,000 repetitions with the function "obtainCompleteGraphsWithVertexOrdering". Using the same data as in the test.
Vertex: 6
Edges: 7
Cliques: 5
Time: 0.488 seconds
Memory: 786,432 bytes

Test 4 - One repetition with the function "obtainCompleteGraphsWithoutPivoting". Using 100 vertex.
Vertex: 100
Edges: 2,507
Cliques: 17,215
Time: 228.430 seconds
Memory: 19,398,656 bytes

Test 5 - One repetition with the function "obtainCompleteGraphsWithPivoting". Using 100 vertex.
Vertex: 100
Edges: 2,507
Cliques: 17,215
Time: 199.249 seconds
Memory: 19,398,656 bytes

Test 6 - One repetition with the function "obtainCompleteGraphsWithVertexOrderingForVertex". Using 100 vertex.
Vertex: 100
Edges: 2,507
Cliques: 17,215
Time: 157.969 seconds
Memory: 19,398,656 bytes

Test 7 - One repetition with the function "obtainCompleteGraphsWithVertexOrderingForVertex". Using 100 vertex.
Selected vertex: 23
Vertex: 100
Edges: 2,507
Cliques: 768
Time: 2.219 seconds
Memory: 4,718,592 bytes

Test 8 - One repetition with the function "obtainCompleteGraphsWithVertexOrderingWithMinimumDegree". Using 100 vertex.
Selected degree: 5
Vertex: 100
Edges: 2,507
Cliques: 13,654
Time: 156.963 seconds
Memory: 16,252,928 bytes

Test 9 - One repetition with the function "obtainCompleteGraphsWithVertexOrderingForVertexWithMinimumDegree". Using 100 vertex.
Selected vertex: 23
Selected degree: 5
Vertex: 100
Edges: 2,507
Cliques: 588
Time: 2.240 seconds
Memory: 4,456,448 bytes