How can I find the count of all possible paths between the 1st node and all other nodes in a directed graph? [on hold]

I want the most efficient algorithm for this problem .

I only want to count all simple paths between the following nodes : - [1,2],[1,3]......[1,n] .

Finally, I want to add them all .

(None of the path should have repeated nodes/cycle(s) )

Constraints : -

1) Every node may only be connected to at most 4 other node(s) which are strictly adjacent, the 'i-th' node will only be connected to either i+1,i+2,i-1,i-2 numbered node in the graph.

2)Graph can contain cycles .

What is the best time complexity I can achieve for this problem?

Example : - 4 nodes , 6 edges : -

(1,2)

(2,1)

(2,4)

(2,3)

(3,4)

(3,2)

(4,3)

Output : - [1,1] + [1,2] + [1,3] + [1,4] = 1 + 1 + 2 + 2 = 6 :)

put on hold as off-topic by user21820, RRL, YuiTo Cheng, José Carlos Santos, Jendrik StelznerJun 13 at 12:14

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