G is a graph with n nodes. Compute the eigenvalues of the Laplacian. If G is connected, then λ1 > 0. If λi= 0 and λi+1 ne 0, then G has exactly i+ 1connected components.

Thank you sir for your answer, That can be used but I think when the graph is large this method has a high complexity, mostly when we have a number of graphs that we need to check if each graph is connected.

The most common technique is to use DFS or BFS.

https://cp-algorithms.com/graph/search-for-connected-components.html

Yes, breadth-first search can be implemented to run in O(|V|+|E|) time, where V is the set of vertices and E is the set of edges. This is best possible.

Thank you all, i will try with BFS

You can use Tarjan's algorithm for graph strongly connected components (based on BFS):

https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm

Hamza Ben Ticha my graph is undirected and Tarjan's algorithm is dedicated to a directed graph as I know it, right?

Benghelima Slimane Charafeddine that's right. A simple way to be able to use Tarjan's algorithm is to transform your graph to a directed one by replacing each edge with two directed edges. Hope this may help !

I will check that because I think this transformation increases the time complexity as the complexity of this algorithm is O(|V|+|E|) where V is the number of vertices and E is the number of edges.

Use the software Gephi .

https://gephi.org/