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

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10
votes
5answers
725 views

Building graph based on the cities connection?

I built a Graph based on the permutations of city's connections from : ...
10
votes
3answers
247 views

Custom edge style (e.g. brush stroke, writing ink, etc.)

I would like to draw a graph with Mathematica in such a way that it looks like a handmade drawing or painting. To be more precise, is there a way to set a custom edge style such that it looks made ...
10
votes
2answers
342 views

Using Gather to rearrange my data

I have a list of elements: {{1, 2}, {1, 5}, {2, 6}, {3, 7}, {4, 8}, {5, 6}, {5, 9}, {9, 13}, {10,11}, {11, 12}, {11, 15}, {15, 16}} I have to divide it into ...
10
votes
3answers
510 views

Label multiple edges between same vertices

I have a simple graph with multiple edges between two vertices, say: Graph[{ Labeled[a -> b, "A"], Labeled[a -> b, "B"] }] Unfortunately, Mathematica ...
10
votes
3answers
954 views

Remove redundant dependencies from a directed acyclic graph

Given a directed acyclic graph, I want to remove all the edges $v_i \rightarrow v_j$ if $v_j$ is reachable from $v_i$ by some other path. Given the rich set of graph algorithms in Mathematica, what is ...
10
votes
2answers
216 views

NumberOfSpanningTrees command not working correctly

I am attempting to use the Combinatorica NumberOfSpanningTrees command for all n-cycle graphs from 3 to 30. I am trying to get a ...
10
votes
2answers
645 views

Proper way to add vertices to an adjacency matrix

I'm looking for a robust way to add vertices to a graph by modifying its AdjacencyMatrix. Here's what I have so far: ...
10
votes
1answer
1k views

Drawing a graph with specified edge lengths

I was wondering if it was possible to ask Mathematica to draw a graph provided some set of vertices: $(v_1, ..., v_N) \in V$ connected by $M$ edges $(e_1, ..., e_M) \in E$, where the length of each ...
10
votes
1answer
191 views

Algorithm used by IsomorphicGraphQ

I'd like to know which algorithm is used to test if two graphs are isomorphic?
10
votes
3answers
318 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: ...
10
votes
2answers
662 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: ...
10
votes
3answers
1k views

How to plot layered graphs?

Given a directed acyclic graph, there is always a possibility to plot the graph as layers, where nodes always send edges into one direction (usually down), to successive layers, and never backwards. ...
10
votes
1answer
88 views

Arrows from GraphicsComplex not converted to Normal form correctly

Bug introduced in 7.0 or earlier and persisting through 10.4.0 Show @ Graph[{1 -> 2, 2 -> 3}, Frame -> True] Normal @ % Is this a pure bug, or have ...
10
votes
1answer
925 views

Roads network visualization by thickness and color intensity by population from GIS files

We can have road networks of the countries in GIS shape file.For exmple from here. Normally traffic flows are proportionate to populations of the cities. I wonder how we can have the same in ...
10
votes
1answer
778 views

When using GraphPlot with an adjacency matrix, how can I make Mathematica draw exactly one self loop for any non-zero weight?

I have tried using the option MultiedgeStyle->None, but apparently Mathematica doesn't treat self loops in the same way it treats edges. For example, I find ...
10
votes
2answers
441 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
4answers
326 views

How can I efficiently check if a graph is unit distance?

A unit distance graph is a graph that is embeddable in the plane so that every edge has length 1. ...
10
votes
1answer
192 views

Issue with PathGraph

I am having a strange issue with PathGraph. Executing PathGraph[{a, b, c}] or ...
10
votes
1answer
396 views

Shortest tour with vertex priority

I changed the title of my question and tried to simplify formulation of the problem. I solve a very big vehicle routing problem. I divided this one big problem on many small sub-problems. Each small ...
10
votes
1answer
343 views

Is there a function to generate a minimal clique cover?

This is a graph problem known as the "Clique Edge Cover" or "Intersection Number" problem, and the goal is to find, from a given graph like $E=\{\{a,b\},\{a,c\},\{b,c\},\{b,d\},\{c,d\}\}$ and ...
9
votes
4answers
510 views

Show path with arrows in a matrix

I have a matrix, for example, 5x5 matrix Partition[Range[25], 5]. And I am given a list, for example: ...
9
votes
2answers
491 views

Sierpinski carpet with GraphData

Is this graph in the list among the so-called "standard" structures used in GraphData? However, I have not found, yet, anything like "Carpet" or "Sponge" in the ...
9
votes
2answers
2k views

Dynamic graph visualisation using JLink/Java and GraphStream

Visualising the addition of new nodes and edges to a graph to 'watch it grow' is to something Mathematica is not suited to by default. However this type of animation really helps convey the emergence ...
9
votes
4answers
306 views

Multiple Forms of Transportation Between Cities

I want to be able to show different connections between cities based on modes of transportation. For instance, you could walk to any city, but it would take a long time, you could take a train, but ...
9
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 ...
9
votes
2answers
528 views

Graphing a network with state transition flows (of varying size)

In one of Stephen Wolfram's recent blog posts (http://blog.stephenwolfram.com/2013/04/data-science-of-the-facebook-world/#more-5350) he provides the network plot below. The size of the arrows that ...
9
votes
3answers
491 views

FindShortestTour for charity (or: How can I optimize meal delivery with FindShortestTour?)

I've been wondering about this for a while - but never got around to asking - until I saw faleichik's incredible answer to Mathematica Minecraft. I did some work at a not-for-profit a little while ...
9
votes
2answers
252 views

Self-loops in Graph may not display correctly or export correctly to PDF (due to BezierCurve problem)

Bug introduced in 10.0 and persisting through 10.3 Problem is due to a BezierCurve bug. I don't understand why the following does not work: ...
9
votes
2answers
357 views

Transition between graphs

I want to visually demonstrate the manipulations made to a graph. For instance, I have a graph g where using the command ...
9
votes
2answers
333 views

VertexSize doesn't scale with Graph layout?

I wonder about how I could make a Graph scale automatically when I vary the size of the vertices. I would like to visualize information with a ...
9
votes
1answer
232 views

Possible improvements to this Syracuse (3x+1)/2 graph?

This algorithm produces the Syracuse disjoint tree graph without any duplicates. No need for Union, For, and ...
9
votes
2answers
1k views
9
votes
1answer
987 views

How to add vertex/edge labels to existing graph

If I have already created a graph using Graph. Later, I want to add to the graph some vertex and/or edge labels, how can I do that? Thank you.
9
votes
2answers
290 views

Relaxation of Mass-Spring System with Pinned Masses

Problem Assume that four masses are connected to each other by springs while two of them are pinned down at their initial positions. Find the position of masses when system is at its minimum ...
9
votes
1answer
347 views

Caching of Graph Graphics

In this answer, Simon Woods concludes that when you display an expression with head graph more than once, something is getting stored somewhere. I looked into it too and found out this only happens if ...
9
votes
1answer
71 views

Cannot set VertexCoordinates twice in a Graph. Workaround?

Versions 10.0-10.2 seem to have a bug when trying to set VertexCoordinates twice on a graph (version 9.0 is fine). Can you confirm it? What is a good workaround ...
9
votes
1answer
138 views

FindHamiltonianCycle is not invariant to edge permutation

Bug introduced in 9.0.1 or earlier and fixed in 10.0 Found this bug-like behaviour today: if the order of edges is changed so that VertexList does not return the ...
9
votes
1answer
721 views

How can I display a multigraph with different colored edges?

I'm new to Mathematica(version 9) and I'm trying to display a multigraph with different colored edges. Here's my code so far: ...
9
votes
1answer
144 views

How to get control over DepthFirstScan?

Is there a way to conditionally take control the flow during a depth-first scan against a TreeGraph? I have a tree graph whose nodes are constructed as object, and there's a method ...
9
votes
0answers
90 views

Set new edge capacity

Bug introduced in 9.0 or earlier and persisting through 10.3.1 I am trying to add a new edge to an existing graph and set its capacity, but for some reason the ...
8
votes
5answers
437 views

Is there a neat way to generate the odd set constraints matrix?

Given a undirected graph $G=(V,E)$, I am trying to generate a related matrix $M$, where columns are indexed by $E(G)$ and rows are indexed by all odd subsets of $V(G)$. I can finish this task using ...
8
votes
3answers
677 views

How can one draw a network with nodes and links in a grid shape?

I'd like to be able to use MMa's graphics to make something like this which I know must absolutely be possible (and probably easy) with MMa. I don't actually even need different colors (though ...
8
votes
3answers
834 views

Visualizing the output of a Voronoi diagram computation

I need to plot a graph (to be specific: Fortune Algorithm output) with given vertex coordinates and a few unconnected vertices. I am thinking of using Mathematica for that. ...
8
votes
3answers
462 views

How to remove all dead ends from a undirected graph?

so what I want to do is take an undirected graph, and remove all the "dead ends" (that is, vertices that are attached to only one other vertex), but do it in such a way that it does it until reaches ...
8
votes
3answers
372 views

Pairwise distances of points and classification using GraphDistanceMatrix

The challenge Given $n$ points in $\mathbf{R}^3$ and a cutoff distance, $d$, I would like to determine all pairs of points that are separated by less than the given cutoff distance, $d$, and all ...
8
votes
3answers
526 views

I can't understand FindShortest Tour

I can't understand the function FindShortestTour because of the result: FindShortestTour[{ {0, 1}, {5, 1}, {2, 1}, {10, 1}}] ...
8
votes
3answers
226 views

How to count all cliques (not just maximal ones) in graphs?

How can I count the numbers of $r$-cliques in a graph? In other words, the number of triangles, the number of $K_4$, the number of $K_5$ etc. I have tried for example ...
8
votes
4answers
364 views

Can I stop edges in graphs from drawing on top of the vertices?

Consider the following testadj = RandomVariate[BernoulliDistribution[0.15], {50, 50}]; AdjacencyGraph[testadj, VertexSize -> Large] The nodes are almost ...
8
votes
2answers
832 views

Controlling TreePlot (and GraphPlot) layout issue

A continuing battle with Mathematica involves graphics heavy with text labels. For example, the following expression renders so that the "Lifecycle properties..." ...
8
votes
3answers
848 views

Random Geometric Graphs

I'm trying to implement an application which uses random geometric graphs in Mathematica, but it seems Mathematica lacks the functionality. I need the following functionalities: Generate a set of ...