# Tagged Questions

Questions about handling graphs in Mathematica, graph theory, graph visualization, GraphPlot, the built-in Graph type and the Combinatorica` package.

3answers
638 views

### Automatically generating a dependency graph of an arbitrary Mathematica function?

Has anyone written a function to pull the function dependencies of a function? That is, it would be nice to have a function that returns a list of function dependencies as a set of rules, terminating ...
2answers
9k views

### How can I use Mathematica's graph functions to cheat at Boggle?

This question is inspired by a Stack Overflow question that I decided to solve using Mathematica. In addition to Mathematica, I thought I'd use some of the new version's graph-related functionality, ...
5answers
2k views

### Custom arrow shaft

Inspired by Sjoerd C. de Vries' nice answer to this question, and the desire to pimp a Graph I did with Mathematica recently I would like to know if there are ways to customize the arrow's shaft ...
1answer
371 views

### Finding the likeliest path in a Markov process

With Mathematica 9, we have the addition of various processes, among which the discrete Markov process. Given a transition probability matrix m, such a process is ...
1answer
349 views

### Reduce distances between vertices of graph to minimum possible?

This simple graph has vertex shapes of different sizes: ...
3answers
1k views

### Finding all shortest paths between two vertices

The built-in FindShortestPath and GraphDistance functions find the shortest path between two particular vertices in a graph. I ...
1answer
303 views

### Strategies for solving problems involving searches

As an example of a search-oriented problem, consider finding all constrained $n$-colorings of a graph. An "$n$-coloring" associates one of $n \ge 1$ colors to each vertex in such a way that no edge ...
1answer
574 views

### How to create regular (planar) graphs?

How to programmatically create and plot regular planar graphs with $k = 3, 4$ or $6$ (not hypercubes) and regular nonplanar graphs of $k = 8$ (see figure)? Note that what matters is the average ...
1answer
906 views

### Is there a way to convert an image into a Graph?

I'm trying to convert an image with several overlapping dots into a Graph. The goal is to be able to derive the Kirchhoff matrix for the randomly created "network ...
1answer
413 views

### Visualizing Rubik's Graph

After the August 2010 discovery that the diameter of the Rubik graph is 20, I wanted to make a way to visualize Rubik's graph. Since there are about $4.3 \times 10^{19}$ vertices in this graph, it is ...
3answers
438 views

### Finding a “not-shortest” path between two vertices

In designing a routine for making a simple three dimensional (5x5x5) labyrinth, I realized that my solutions (a solution is a labyrinth includes a single path from {1, 1, 1} to {5, 5, 5} in a 5 x5x5 ...
2answers
939 views

### Cycles of length N in a graph

If I have an undirected graph represented with an adjacency matrix, how can I find all the subgraphs which are a cycle of length N? I don't really know the math nor the programming language well, so ...
2answers
737 views

### How to plot planar graphs as such?

A planar graph is a graph that can be drawn in the plane such that no two edges cross. For example, the graph ...
4answers
503 views

### How can I replace bi-directional DirectedEdge pairs in a Graph with a single UndirectedEdge?

The Cayley graphs produced by Mathematica 8.0's CayleyGraph function represent actions that are their own inverses in an unconventional way: rather than using a ...
2answers
1k views

### How to play with Facebook data inside Mathematica?

I saw this post from Wolfram here and I would like to know how to import facebook data into Mathematica.
1answer
176 views

### Is UndirectedEdge[a,b] the same edge as UndirectedEdge[b,a]?

Is UndirectedEdge[a,b] the same edge as UndirectedEdge[b,a]? Then please consider this. ...
3answers
662 views

### How to generate a random tree?

Is it possible to generate a random tree without explicitly constructing a random adjacency matrix that satisfies tree properties? How about a random directed tree? Edit: incredible answer by ...
3answers
322 views

### How to get complete Documentation Center graph of guide pages?

On the very last image below you can see a typical path of walking through Documentation Center guide pages. What is the best way to get the graph data and visualize the whole structure of these ...
3answers
714 views

### Generating graphs interactively (GUI)

I want to create graphs interactively using a GUI. I thought of using a ClickPane[] environment. The code I have (in part borrowed from the Documentation) works ...
2answers
241 views

### Packed Graph or GraphPlot output with non-square layout?

Graph or GraphPlot produce square layouts for disconnected graphs: Graph[Table[i -> Mod[i^3, 100], {i, 1, 100}]] I´d like to get a rectangular layout with ...
1answer
413 views

### How to export and import Graphs with additional data?

I'm trying to export and then later import graphs with additional data added such as VertexLabels and EdgeLabels. When I export ...
1answer
263 views

### Convert GraphPlot[]s with many nodes into something that's human-understandable

This is more of an abstract/creative problem. I think everyone who has played around with GraphPlot, ended up with an image that looks like this, at least once in ...
3answers
1k views

### How to generate random directed acyclic graphs?

How to programmatically build random directed acyclic graphs (DAG)? I know about the AcyclicGraphQ predicate and the ...
1answer
411 views

### Graph vs GraphPlot

What is the difference (in purpose) between Graph and GraphPlot? Which function is bested suited to which tasks? Background: I ...
1answer
299 views

### Need tips on improving this directed graph

First we define a function that returns the least odd prime factor. lopf[n_] := FactorInteger[n][[2, 1]] Then we craft a routine that performs the 3x+1 steps ...
2answers
445 views

### Graph layout on a grid

Is it possible for Mathematica to layout a graph so that the connections lie on a grid? Furthermore, for graphs with multiple edges per vertex, is it possible to specify the location on the vertex ...
3answers
727 views

### How to get graph layout that reflects edge weights?

My heart soared to discover that Mathematica 8 offers support for specifying a weighted adjacency matrix in WeightedAdjacencyGraph. But it seems that, regardless of the weights between edges, the ...
2answers
377 views

### How can I speed up the classic GA for graph coloring?

I'm trying to compute the chromatic number of this graph (which is 28): g = Import@"http://www.info.univ-angers.fr/pub/porumbel/graphs/dsjc250.5.col"; My genetic ...
1answer
280 views

### When to use built-in Graph/GraphPlot vs. Combinatorica

What are the pros and cons of using built-in Graph/GraphPlot (and related) types vs. types in the Combinatorica package?
4answers
325 views

### How can I remove B -> A from a list if A -> B is in the list?

I have a list of transformations like this: list = {"A" -> "B", "B" -> "A", "C" -> "D"} As this is used to plot an undirected graph with ...
3answers
396 views

### How to find all vertices reachable from a start vertex following directed edges?

How to find all vertices reachable from a given start vertex following directed edges, in a cyclic directed graph given as ...
3answers
511 views

### Creating diagrams for category theory

Lately I've been doing algebra and I have found myself drawing a bunch of diagrams when I attempt to solve a problem. Most of the diagrams are very simple so I thought, I bet I can do this in ...
3answers
336 views

### Determining all possible traversals of a tree

I have a list: B={423, {{53, {39, 65, 423}}, {66, {67, 81, 423}}, {424, {25, 40, 423}}}}; This list can be visualized as a tree using ...
2answers
313 views

### How to measure segment length and branch angle

I am trying to measure segment length and branch angle or bifurcation angle between each pair of segments. My image after thinning looks like this: ...
1answer
259 views

### Visiting nodes in a tree bottom up

I have a problem that can be reduced to this one: Suppose I have an unbalanced (almost random) tree. The leaves of the tree have one property already set, and all vertex (including the leaves) have ...
2answers
124 views

### What is the most convenient way to change options for Graph[] objects?

What is the most convenient way to change options such as VertexLabels in existing Graph objects? (Version 7 users note: ...
2answers
846 views

### Solving the Travelling Salesman Problem

I've been trying to find some kind of mathematical computer software to solve the Travelling Salesman Problem. The Excel Solver is able to do it, but I've noticed there is a built-in function in ...
2answers
220 views

### Comfortable Edge Labeling of Undirected Graph

I'm working on a program that finds special [called "interval"] edge-colorings for graphs. Output is as follows: ...
1answer
114 views

### How can I conveniently call igraph through RLink?

Mathematica has lots of functions for working with graphs, but this functionality is not yet as mature as the igraph library. It is useful to have access to igraph from Mathematica, both for ...
1answer
349 views

### Drawing Graph Products

I need to draw graphs that are Cartesian products of 2 graphs. I need them to look like this: . So each copy of the factors can have LinearEmbedding, but the whole ...
2answers
770 views

### Simple algorithm to find cycles in edge list

I have the edge list of an undirected graph which consists of disjoint "cycles" only. Example: {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {5, 6}, {6, 7}, {7, 5}} Each ...
3answers
310 views

### How to recompute the layout of a Graph?

I asked a question about changing Graph properties in a similar way to how Show can change ...
2answers
683 views

### How to convert an image to a graph and get the positions of the edges?

I am trying to convert an image to a graph. My image is already skeletonized and looks pretty much like this: What I need to do is identify all vertices and edges, and in particular get a list of ...
2answers
374 views

### Calculating morphometric properties

Is it possible to calculate segment length, segment diameter and branch angles for three dimensional geometry. Geometry contains vertex points and polygon surfaces as ...
1answer
127 views

### Layout a second graph of the same nodes in the same way

I have a number of graphs with the same nodes. I would like to be able to somehow save the layout that results from the spring embedded results of one graph (the first image), and have the other ...
1answer
376 views

### How to divide a graph into connected components?

Suppose I have some edges: edges = {1 -> 2, 2 -> 3, 3 -> 1, 4 -> 5, 3 -> 6, 7 -> 8, 8 -> 9, 8 -> 10}; And I make a graph: ...
1answer
178 views

### Ulam's Spiral with Opperman's diagonals (quarter-squares)

First we craft a function to return the quadrant boundary based on Oppermann's Conjecture a[n_] := (Mod[n, 2] + n^2 + 2 n)/4 Then we create a few lists ...
1answer
351 views

### Use Mathematica to do a network analysis of Mathematica.SE

Recently Wolfram|Alpha announced that you could use it to analyze your Facebook site. How could I do a network analysis of questioners and answers here on Mathematica.SE?
2answers
195 views

### Listing subgraphs of G isomorphic to SubG

If I have an undirected graph G, how could I write a function in Mathematica to obtain a list of subgraphs of G that are isomorphic to some other undirected graph SubG? I'd like to learn how to ...
4answers
322 views

### Ordering vertices in GraphPlot

I'm new here, so forgive me if this question is not well-posed/duplicates an earlier question - although I've searched for similar questions without success. I'm trying to present a plot of ...
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