Problem 2646. Determine the number of maximal cliques in an undirected graph

In an undirected graph, a clique is a subset of vertices that are fully connected, i.e. there is an edge between all pairs of vertices in the subset. A maximal clique is one in which the subset of vertices is not part of a larger clique. So, for instance, a fully connected graph has many cliques, but only one maximal clique.

Given an NxN adjacency matrix (A) for an undirected graph with N vertices, return the number (num) of maximal cliques.

Example

Consider the graph shown below,

which has the following adjacency matrix:

A = [ 0 1 0 0 0
      1 0 1 1 0
      0 1 0 1 0
      0 1 1 0 1
      0 0 0 1 0 ]

The number of maximal cliques is 3. The maximal cliques are {1,2}, {2,3,4}, and {4,5}.

NOTE: You may assume the data type of the adjacency matrix is double.

Solution Stats

58.33% Correct | 41.67% Incorrect
Last Solution submitted on Nov 05, 2023

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers6

Suggested Problems

More from this Author44

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!