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Number of complete subgraphs in a given undirected graph

原文 2016-09-04 05:39:44 7 1 algorithm/ graph-theory

What is the best approach to find the number of complete sub-graphs with maximum number of nodes possible, given an undirected graph?
PS: By complete I meant that every node is connected to every other node with an unique edge.

1 answers

You are talking about Clique Problem , this is a classical computer science problem, it is NP Complete. Which means that it doesn't have any solution to it, which could run on today's computers in polynomial time .

Although, approximation algorithms exist to give a solution, they are weak.

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Related Question What's the best algorithm for extracting all unique, complete subgraphs from an undirected graph of perhaps 1,024 nodes? Algorithm to partition graph into complete subgraphs Maximum number of subgraphs of a graph How can I find the number of Hamiltonian cycles in a complete undirected graph? Finding the number of paths of given length in a undirected unweighted graph Number Of Cycles In a Undirected Graph Given an undirected graph G = (V, E), determine whether G is a complete graph Is the problem of finding the simple path with maximum cost in a weighted undirected graph with the same number of vertex and edges NP-Complete? Maximize number of subgraphs with a given minimum weight subgraphs in a graph

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Number of complete subgraphs in a given undirected graph

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1 answers

solution1 1 2016-09-04 05:47:10

solution1
1 2016-09-04 05:47:10