11 fixed formatting
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**Step 3 - Give every vertix a path dependent name (EDITED to be label each vertex with a path list) **Step 3 - Give every vertix a path dependent name (EDITED to label each vertex with a path list). For example, the path list {1,5,3,2} can be relabeled as {{1},{1,5},{1,5,3},{1,5,3,2}}. These labels will help us group all 1->5 paths in the first step together.

**Step 3 - Give every vertix a path dependent name (EDITED to be label each vertex with a path list) **. For example, the path list {1,5,3,2} can be relabeled as {{1},{1,5},{1,5,3},{1,5,3,2}}. These labels will help us group all 1->5 paths in the first step together.

Step 3 - Give every vertix a path dependent name (EDITED to label each vertex with a path list). For example, the path list {1,5,3,2} can be relabeled as {{1},{1,5},{1,5,3},{1,5,3,2}}. These labels will help us group all 1->5 paths in the first step together.

10 corrected typos within intro
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@AntonAntonov's answer with the TriesWithFrequencies.m package is more elegant and useful that calculates deadlocks in the , but here is a brute force approach without any extra packages.

@AntonAntonov's answer with the TriesWithFrequencies.m package is more elegant and useful that calculates deadlocks in the , but here is a brute force approach without any extra packages.

@AntonAntonov's answer with the TriesWithFrequencies.m package is more elegant and useful, but here is a brute force approach without any extra packages.

9 fixed typos in module (where exampleGraph should have been graph), added butterfly graph example
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UPDATE: Example with more than 10 vertices

ButterflyGraph[2, VertexLabels -> "Name", ImageSize -> Medium]
pathTreeGraph[ButterflyGraph[2], 1, 2]

enter image description here enter image description here

UPDATE: Example with more than 10 vertices

ButterflyGraph[2, VertexLabels -> "Name", ImageSize -> Medium]
pathTreeGraph[ButterflyGraph[2], 1, 2]

enter image description here enter image description here

8 fixed typos in module (where exampleGraph should have been graph)
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7 Generalized to label vertices with lists (to allow more than 10 nodes) and made labels clearer
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6 added 135 characters in body
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5 deleted code summary (redundant given module form)
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4 added module implementation
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3 added maxVertexValue to make code a little more general
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2 referenced better answer and provided some context for this approach
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1
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