how to find all aliques of a node from an adjacency matrix?

i ran into a problem that find all cliques that a node have...

for example, here's an adjacency matrix:

X = [0 1 1 1 1
    1 0 1 1 1
    1 1 0 1 0
    1 1 1 0 0
    1 1 0 0 0];

1 means the two nodes can connect and 0 is the opposite meaning.

all the cliques that the first node have is [1 2 3 4] and [1 2 5], and that's the result i find by drawing a picture instead of by coding. my question is how to code and find the result?

i totally have no idea😭if anyone helps me, thanks a lot!!!

Answer 1

[Jaynik]

Hi @rumin diao,

A clique is a collection of vertices in an undirected graph G such that every two different vertices in the clique are adjacent. There is no direct function in MATLAB to find cliques. However, you can implement a custom script to achieve this. By studying algorithms available in other programming languages, you can adapt their logic to MATLAB.

If you want to find maximal cliques, you can try to use these file exchange implementations of the Bron-Kerbosch algorithm:

• https://www.mathworks.com/matlabcentral/fileexchange/30413-bron-kerbosch-maximal-clique-finding-algorithm
• https://www.mathworks.com/matlabcentral/fileexchange/47524-find-maximal-cliques-for-large-sparse-network

Hope this helps!