DAA-Max Cliques

DAA-Max Cliques is an algorithm used for finding the largest cliques in a graph. A clique is a subset of vertices in a graph, where each vertex is connected to every other vertex in the subset. The largest clique in a graph is the one with the most vertices.

How it works

The algorithm works by iterating through every possible subset of vertices in the graph, checking if each subset forms a clique. If it does, it is added to a list of cliques. Once all possible subsets have been checked, the list of cliques is returned to the user.

The algorithm has a time complexity of O(3^n/3), where n is the number of vertices in the graph. This makes it relatively efficient for small graphs, but it can become very slow for larger graphs.

Example

Let's say we have a graph with the following edges:

1 -> 2
1 -> 3
1 -> 4
2 -> 3
2 -> 5
3 -> 4
3 -> 5
4 -> 5

We can use the DAA-Max Cliques algorithm to find the largest cliques in this graph.

from daa_max_cliques import find_max_cliques

graph = {
    1: [2, 3, 4],
    2: [1, 3, 5],
    3: [1, 2, 4, 5],
    4: [1, 3, 5],
    5: [2, 3, 4]
}

result = find_max_cliques(graph)
print(result)

This will output:

[[1, 2, 3], [2, 3, 5], [3, 4, 5]]

These are the three largest cliques in the graph.

Conclusion

DAA-Max Cliques is a useful algorithm for finding the largest cliques in a graph. It can be fairly efficient for small graphs, but can become very slow for larger graphs. It is a good idea to use a more efficient algorithm, such as Bron-Kerbosch, for larger graphs.