StackOverflow2013

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2013-03-03T00:17:10.943
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2013-03-03T00:50:55.520
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Body
The first problem you might encounter in an attempt to put your operations in a mathematical description is your definition of the "shortest cycles" as cycles are typically defined as a sequence of vertices connected by edges in which the first one is also the last one. <h2>Math crashcourse</h2> In math a graph is typcally described by two sets V (like vertices) and E (like edges) The set E consisting of sets with two elements each of them being a vertex. Such as <ul> <li>V = { v1, v2, ...., vn }</li> <li>E = { ..., {vi, vk}, ... }</li> </ul> Every set in E correspends to one edge in your graph. As such a (connected) path is typcially defined as: A sequence of vertices v1, ...., vn with the property that for every two consecutive vertexes in the sequence vi and vi+1 the set { vi, vi+1 } is an element of the set E. (practically speaking: there is an edge from vertex vi to vertex vi+i) A cycle is typically defined as a path with the property: v1 = vn (thus the first vertex is also the last one) Whith this definition an your example already the sequence: 1, 4, 1 forms a cycle (in the mathematical sense) As such every edge in your graph would count as a "shortest" cycle, while the examples given are definately longer! You told that you <blockquote> ... neglect the cycles whose length is less than 3 </blockquote> this doesn't look to bad as a starting point for your description. Unfortunately I didn't completely understand the next steps you want to perform. <h2>Advice</h2> My advice, or the least the way I would approach the problem is to convert the rather long description to some kind of shorter algorithmic description while refining on exactly how you try to perform the task. This way getting to your final description shouldn't be too hard to accomplish. Especially don't forget to tell what exactly the input to your algorithm is. Even that doesn't seem to be too clear from your description. <ul> <li>are you starting with a already known set of "shortest" cycles?</li> <li>or are you just given a graph as input and have to determine the "shortest" cycles yourself?</li> <li>if you detect them yourself how exactly is this done? Especially don't forget to tell about this part of the story if it applies as it seems to be one of the most crucial ones to your problem.</li> </ul>
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singulars
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1. This table or related slice is empty.
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1. POsplitting of a graph into cycles and then into paths
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