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

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1

1

$begingroup$

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 :)

graph-theory

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edited 14 hours ago

Firex secred

asked 15 hours ago

Firex secredFirex secred

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Firex secred is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment | 

1

1

$begingroup$

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 :)

graph-theory

share|cite|improve this question

edited 14 hours ago

Firex secred

asked 15 hours ago

Firex secredFirex secred

112

New contributor

Firex secred is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

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 :)

graph-theory

share|cite|improve this question

edited 14 hours ago

Firex secred

asked 15 hours ago

Firex secredFirex secred

112

New contributor

Firex secred is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 14 hours ago

Firex secred

asked 15 hours ago

Firex secredFirex secred

112

New contributor

Firex secred is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited 14 hours ago

Firex secred

asked 15 hours ago

Firex secredFirex secred

112

New contributor

Firex secred is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 15 hours ago

Firex secredFirex secred

112

New contributor

Firex secred is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 15 hours ago

Firex secredFirex secred

112