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

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53
votes
2answers
10k views

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

Boggle is a word game played with 16 dice and a 4x4 tray. This question is inspired by a Stack Overflow question about Boggle that I decided to solve using Mathematica. In addition to Mathematica, I ...
21
votes
2answers
1k views

How can I conveniently call igraph from Mathematica?

Mathematica has lots of functions for working with graphs and networks, but there are still some functionality holes that are provided by other packages. Also, due to the nature of graph theory, ...
70
votes
3answers
2k 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 ...
15
votes
6answers
519 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 ...
29
votes
3answers
2k 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 ...
25
votes
5answers
4k 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 ...
16
votes
4answers
626 views

Can TreeForm be displayed “sideways”?

One recurrent problem I'm having with displays generated with TreeForm is that the expressions to be so displayed often at least one level with many (> 20) nodes at,...
24
votes
3answers
3k 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 ...
12
votes
1answer
1k views

How to speed up Minimum Spanning Tree algorithm?

How to speed up MST algorithm? I work with graphs and I have adopted Prim's algorithm for my needs, from here. The graphs which I use are very dense (number of vertexes: $V=500$ and every vertex is ...
25
votes
2answers
5k 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.
31
votes
4answers
6k 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 ...
14
votes
1answer
531 views

Transform an expression into a graph that can be plotted with TreeGraph (not TreeForm)

I would like to plot an expression (like TreeForm does), but using the new TreeGraph functionality. ...
10
votes
3answers
1k views

Finding face vertices from the face adjacency graph

I have a question about face adjacency graphs. Suppose that I have an adjacency matrix ...
6
votes
2answers
285 views

Is there something wrong with VertexConnectivity

Note: this is fixed in version 10. As I noticed in the documentation VertexConnectivity is defined as the following The vertex connectivity of a graph $g$ is ...
34
votes
5answers
10k 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 ...
17
votes
4answers
20k views

Finding all simple paths between two vertices in a graph

There are built-in methods to find a shortest path between two vertices in a graph, and the question on finding all shortest paths between two vertices has gathered quite a bit of attention. A path ...
18
votes
2answers
6k 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 ...
18
votes
5answers
1k views

Graph from binary matrix (not adjacency) respecting the original matrix positions

I have a binary matrix. My objective is to connect every close (without "jump") elements with value equal to 1, but I must keep the point positions, just like it's shown at the image. Can somebody ...
17
votes
4answers
1k 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 ...
17
votes
3answers
6k 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 ...
14
votes
2answers
2k 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 ...
26
votes
2answers
3k 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 ...
7
votes
2answers
809 views

How to add new nodes to an existing graph with fixed (coordinates) nodes?

I'm ultimately trying to create a directed graph with some of the nodes in fixed positions and the other nodes placed around them in "acceptable" positions. It's better if I ask the question by ...
14
votes
4answers
2k views

Finding elementary cycles of (directed) graphs

I need to enumerate all the simple cycles (i.e. elementary cycles where no vertex is repeated other than the starting) of a graph which has both directed and undirected edges, where we can treat the ...
8
votes
2answers
309 views

Cases[data,Colon[key,_]] vs. Cases[data,key:_] toward XPath, XQuery

Exploring methods to index and search tree-structured key:value pairs via named-entity index (key paths) as opposed to Position-based indexing. Using Rule as <...
6
votes
3answers
278 views

Converting expressions to “edges” for use in TreePlot, Graph

This question is similar to this: Nested list to graph. How to "flatten" an arbitrary expression, eg expr = a[b[c, d[e][f], g], h] to a list of key-value pairs ...
10
votes
3answers
329 views

Preserving labels when using graph functions

I am finding that some functions that accept a graph and return a transformed graph lose all the vertex and edge labels of the graph being transformed. For example, when I define a graph like this: <...
32
votes
1answer
2k 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 ...
24
votes
2answers
2k views

Drawing pairs (planar graph, circle packing)

Circle packing theorem states: For every connected simple planar graph G there is a circle packing in the plane whose intersection graph is (isomorphic to) G. How to use Mathematica to draw examples ...
9
votes
2answers
1k views
11
votes
1answer
545 views

Dynamic visualization of Graph[] on a webpage

How can we embed a dynamic version of a Graph object on a web page, similar to the one showcased on the networkx home page? This sort of dynamic visualization can ...
25
votes
1answer
1k views

Graph vs. GraphPlot

What is the difference (in purpose) between Graph and GraphPlot? Which function is bested suited to which tasks? Background: I ...
19
votes
5answers
1k 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 ...
15
votes
2answers
2k views

Creating a graph with variable size of vertices and variable thickness of edges

I'm trying to create a graph to represent transitions between different states of a system. I would like to represent the time the systems spent in a state with the size of the vertex and the ...
17
votes
4answers
333 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: ...
12
votes
2answers
428 views

Determining whether two $k$-chromatic graphs are isomorphic (respecting vertex coloration)

Consider the case where I have two $k$-chromatic graphs $G_1$ and $G_2$, i.e. two graphs where individual vertices can be colored with one of a set of $k$ total colors, and I would like to determine ...
12
votes
2answers
826 views

Convert Graph to Graphics

In Mathematica 9, a graph is returned as an object with head Graph: In[1]:= CompleteGraph[8] // Head Out[1]= Graph Right-...
10
votes
2answers
452 views

Removing edge weights from a Graph

How can I remove EdgeWeights from a Graph without affecting any other properties of the graph? Let's construct a graph with ...
10
votes
2answers
681 views

HighlightGraph with different styles

I want to highlight two different directed paths on a graph with two different style. I am using the following two code snippets: ...
4
votes
1answer
647 views

Isomorphisms for graphs with loops and multiple edges

I am working with graphs with multiple edges and loops, and I want to eliminate all isomorphic graphs from a long list I've generated. The FindGraphIsomorphism ...
11
votes
4answers
845 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 ...
11
votes
2answers
254 views

Vertex descendants subgraph

Keywords: vertex, ancestors, descendants, subgraph, directed graph, flow subtree So let's say we have a TreeGraph: ...
7
votes
3answers
356 views

Drawing a graph with vertex avoiding edges? (Handling vertices that must be colinear?)

I'd like to draw something like the following graph: ...
7
votes
2answers
1k views

Coloring edges in GraphPlot

I'm a little stuck with graph drawing part of my research — I can't use the Graph function for plotting my graphs, because my graph is a multi-graph. ...
5
votes
3answers
1k views

How to find all graph isomorphisms in FindGraphIsomorphism

I found the second definition of the function FindGraphIsomorphism not working. Here's the definition Mathematica 8 gives: ...
26
votes
2answers
2k views

Trying to Visualize a Collatz - The Collatz conjecture

I happen to have this collatz collatz[x_, y_] := If[x == 3*y || x == 2*y + 1 || y == 3*x || y == 2*x + 2, 2, 0] So i want a visual 3D adjacency graph of my ...
23
votes
1answer
757 views

How to visualize large graphs with directed edge bundling?

I'm wondering if anyone has implemented edge bundled graph plotting? An important paper is "Force-Directed Edge Bundling for Graph Visualization" by Danny Holten and Jarke J. van Wijk.
22
votes
2answers
1k 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 ...
14
votes
3answers
609 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 ...
24
votes
4answers
594 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 ...