Problem 1170. Count the Number of Undirected Cycles in a Graph

Created by Joseph Kirk

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Last Solution submitted on Dec 11, 2019

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Alfonso Nieto-Castanon on 4 Jan 2013

could you please clarify, in your example, why cycles like '1->2->1', '1->5->1' or '3->5->3' are not counted?

Alfonso Nieto-Castanon on 4 Jan 2013

it seems the expected solution only counts cycles that include three or more nodes... is this correct?

Joseph Kirk on 5 Jan 2013

That is correct. In a directed graph, the cycle 1 -> 2 -> 1 actually uses two different edges, while in an undirected graph, the edge 1 -> 2 and 2 -> 1 are one and the same. I am only considering cycles valid if each node along the way is visited once and if edges are not used more than one time. I chose this criteria so that the number of cycles counted would match the results for the table provided here: http://mathworld.wolfram.com/GraphCycle.html

Alfonso Nieto-Castanon on 5 Jan 2013

got it. Thanks for the clarification!

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Solution 472008

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Clark Grismond on 18 Apr 2015

Can you please send me your code for this??? Really struggling on this for a school assignment clarkieg123@gmail.com

Solution 186443

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Clark Grismond on 18 Apr 2015

Can you please send me your code for this??? Really struggling on this for a school assignment clarkieg123@gmail.com

Solution 185908

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1 Comment

Clark Grismond on 18 Apr 2015

Can you please send me your code for this??? Really struggling on this for a school assignment clarkieg123@gmail.com

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cycles graph theory undirected graphs

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Problem 1170. Count the Number of Undirected Cycles in a Graph

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Problem 1170. Count the Number of Undirected Cycles in a Graph

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