Question

I’m using Ruby and the Ruby Graph Library http://rgl.rubyforge.org/

How do I find all the cliques (complete subgraphs) in a graph?

Specifically, I’m looking for a 5 clique involving two particular vertices.

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What I’m really up to – Project Euler Problem 60

The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property.

Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.

My graph has vertices the prime numbers, with an edge from p to q if decimal concatenations ‘pq’ and ‘qp’ are both prime.

Answer 1

Specifically, I’m looking for a 5 clique involving two particular vertices.

Assuming those two vertices are first and second

common = ug.adjacent_vertices(first) & ug.adjacent_vertices(second)

for triple in common.combination(3)
    a,b,c = triple
    if ug.has_edge?(a,b) && ug.has_edge?(a,c) && ug.has_edge?(b,c)
        return [first,second,a,b,c]