Implementation of https://en.wikipedia.org/wiki/Bron–Kerbosch_algorithm

The Bron–Kerbosch algorithm is an enumeration algorithm for finding all maximal cliques in an undirected graph.

A clique is a subset of verticies in a graph such that all the verticies are connected by an edge.

A maximal clique is a clique such that no more verticies could be added to it while preserving the clique property.

This example shows the expected output on a simple graph. The example uses an inefficient graph input representation to keep the example simple.

    ┌─┐   ┌─┐
 ┌──│4│───│5│──┐
 │  └─┘   └─┘  │
┌─┐  │     │  ┌─┐
│6│  │     │  │1│
└─┘  │     │  └─┘
    ┌─┐   ┌─┐  │
    │3│───│2│──┘
    └─┘   └─┘

>>> let adjList = [(1,2),(1,5),(2,3),(2,5),(3,4),(4,5),(4,6)]
>>> maxCliques (\x y -> (min x y, max x y) `elem` adjList) [1..6]
[[1,2,5],[2,3],[3,4],[4,5],[4,6]]