A graph with maximum number of strongly connected components

Question

Create a directed graph with 6 nodes (say) such that it has maximum number of strongly connected components.

• For example, take complete graph with 4 nodes with all edges connected. This is graph has only 1 strongly connected component, i.e entire graph is a single component.

The objective is to maximise the number of components.

Answer 1

Your question does not make sense as posted.

Best guess: you want to create a new graph with a given number of nodes that will have the maximum number of strongly connected components. Edges can be added between any pairs of nodes.

The smallest strongly component is a pair of nodes with an edge going in each direction between them.

So the maximum number of components in a graph with N nodes will be N / 2

e.g. a 4 node graph with two components has edges between

1 2
2 1
3 4
4 3
1 3