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

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8
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3answers
380 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
541 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
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3answers
253 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
370 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
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2answers
862 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
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3answers
869 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 ...
8
votes
2answers
370 views

Is there a bug in FindClique?

If h is a graph, FindClique[g, {n}] should return a clique on exactly $n$ vertices if one exists in ...
8
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2answers
353 views

Organise a graph's vertices into levels

I would like to organise a graph's vertices in levels. Consider ...
8
votes
2answers
269 views

Constructing a graph from a distance matrix

I have a set $S$ of $n$ 2-dimensional points. We can compute a distance matrix (Euclidean distance) for $S$ using say this answer. I wish to form an $n$-vertex graph having the points $S$ as vertices, ...
8
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2answers
388 views

How do I convert this Nicomachus's Triangle to one with edges?

I want to put edges on this Nicomachus's Triangle r = 7; t = Table[2^(n - k) 3^k, {n, 0, r}, {k, 0, n}]; ColumnForm[t, Center] Is there an easy way to do this? ...
8
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1answer
479 views

Coloring edges of a graph according to their weight?

What's the simplest way to plot a graph with weighted edges, such that the color of the edge corresponds to the weight of the edge?
8
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2answers
307 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 <...
8
votes
2answers
217 views

Efficient solution for a discrete assignment problem with pairwise costs

Let's consider a simple graph with N vertices, and a corresponding set of N items. The goal of the problem is to assign every item to a vertex on the graph so that sum of a per-edge (that is item-...
8
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2answers
421 views

Creating a hyperlink graph from Wikipedia

This goes out to all the Mathematica experts - I'm hoping to get some helpful comments, ideas or code for that matter. In my attempts to maximize learning efficiency I had the idea to create an (...
8
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2answers
417 views

Colorize and the Four-Color Theorem

We can write: MorphologicalComponents[image] // Colorize To assign a random set of colors to each component in some image. The example used for reference by ...
8
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2answers
4k views

How to find the Shortest Path, visiting ALL vertices, without coming back to the start (Hamiltonian Path, minimum distance)

A car has to pick up each person and take them to their destination. I am trying to find the shortest tour that will do this. How can I find the shortest path between any s and t.... visiting all ...
8
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2answers
238 views

Plot a 3-cycle graph with clockwise-directed edges

When I try to plot a 3-cycle, the edge direction is always counter-clockwise. The plotting code is ...
8
votes
1answer
165 views

Alignment of `TreePlot`

I want to construct a binomial tree using TreePlot but have troubles with the alignment. The code ...
8
votes
1answer
182 views

Using GraphHighlight interactively

I want to build a small GUI, where the user can select either a single edge or a single node of a graph. I got to this point: ...
8
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3answers
115 views

Tree graph showing all simple paths with dead ends between two vertices in undirected graph

I have undirected weighted labeled graph. How i can generate and visualize tree graph, showing me all simple paths (and dead ends) from vertice A to vertice B? For example, for this graph to show ...
8
votes
1answer
371 views

How can I sequentially apply different graph embeddings?

Imagine I have some graph G, and I perform a graph embedding using a command like: ...
8
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3answers
485 views

TreePlot with centered vertexes

I want to draw a tree plot for Euler totient function for this question like the following: I generate the EulerPhi for first 20 numbers into a list: ...
8
votes
1answer
231 views

Vertex merging in graph?

Given a Graph such as the one produced with the following code ...
8
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2answers
421 views

Finding All Chordless Simple Cycles In A Graph

I am doing a research on networks which consists of polygons with different number of sides. I am trying to find all simple cycles in a network which are chordless. As an example, consider the ...
8
votes
1answer
617 views

Why does SocialMediaData return such a small FollowerNetwork?

I have hooked up my Twitter account to Mathematica and I have 1468 followers myfollowers = Length[SocialMediaData["Twitter", "Followers"]] 1468 I wondered what ...
8
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1answer
218 views

Enforce graph symmetry

I am using ...
8
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1answer
1k views

Dynamic Graph visualization

I'm working on a C++ library that will be used to construct and study certain graphs (as in a set of connected vertices, not a function plot). These graphs will be dynamic in nature (and can ...
8
votes
1answer
97 views

Smallest connected subgraph containing all given vertices

Given a connected graph $G$ and a subset of its vertices, $S$, I need to find the smallest connected subgraph of $G$ containing all of $S$. How would you approach this in Mathematica? I am asking ...
8
votes
1answer
80 views

Is there an easy way to set or retrieve a graph edge properties as a list, in a single go?

I am trying to use arbitrary edge properties in Graphs, and I am looking for easy ways to work with them. In many cases it would be convenient to be able to set ...
8
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0answers
131 views

Exporting a high-resolution GraphPlot of a very large graph (65,536 nodes)

Problem I have a very large graph of 65,536 vertices. GraphPlot yields: But the vertices are too dense to see in any detail, and attempting to use any of the on-...
8
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0answers
111 views

Deleting zero edges from a graph causes bizarre behavior

Bug introduced in 10.3.0 and fixed in 10.4. Consider the following (very simple) graph, with two vertices and one edge: g = Graph[{1, 2}, {1 <-> 2}]; I ...
8
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0answers
89 views

More efficient way to generate lattice graph with edges between visible vertices?

Given a nXn lattice, I need to generate the graph such that there is an edge between two vertices iff they are directly "visible" to each other, i.e., there is no vertex between them. I'm using <...
8
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0answers
92 views

Graph: PropertyValue changes and Dynamic

I almost never work with Graph in Mathematica but lately I helped someone with it. For this, I tried to make an animation using ...
7
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3answers
370 views

Converting Mesh in Density Plots to a Graph

Consider the following line of code: ...
7
votes
3answers
2k views

Travelling salesman with start and end points for 30 points

I am doing a route optimisation for delivery vehicles and failing dismally. Please see problem statement below. My current solution uses FindShortestTour, but this does not have defined start and end ...
7
votes
3answers
339 views

Test if directed graph is connected

Is there a simple built-in way to check if a directed graph is connected? Now, before you throw ConnectedGraphQ or ...
7
votes
2answers
1k views

Is it possible to export a graph as graphic to Excel?

It is straightforward to export lists to Excel with Export. Can I export a graphic image, too? This does not work: ...
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3answers
348 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
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3answers
438 views

Different colors for nodes in tree plot

I have some list of numbers which I am plotting using TreePlot. This is the code: ...
7
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2answers
317 views

How to make each node of a graph a button?

A newbie question this one - MMA help seems to suggest it would be possible to place a button on ( or have a button be ) each node of graph, labelled with the name of said node. I have no idea where ...
7
votes
2answers
720 views

Can I put tooltips in a Graph?

This doesn't work: Is there a way to do this? My real goal is to identify the second links in the graph below, which shows the results of a webcrawl (using this code). I'm open to another ...
7
votes
1answer
163 views

Replacing graph nodes with matrices

I would like to label a graph with matrices. Suppose the graph is simple: And I have an array mats that contains the labels for vertices 1,2,3,4 (these are just random 0-1 matrices; ignore the ...
7
votes
2answers
315 views

Is there something akin to “SubgraphIsomorphismQ” in Mathematica 9?

Provided two unlabeled graphs, $G$ and $H$, I would like to test where $H$ is a subgraph of $G$. In other words, I'd like to test whether we can prune some fixed number of vertices or edges from $G$ ...
7
votes
2answers
607 views

Edge problems in a directed graph

I want to create the following two graphs. So far I tried the following Code ...
7
votes
1answer
268 views

Fractal dimension of a large networked molecular system

I am trying to determine the fractal dimension of this complex biomolecule (figure attached). Any clues as to how this can be done. In trying to determine this quantity, I wonder how its ...
7
votes
2answers
994 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. ...
7
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4answers
429 views

Automatically convert pairs of directed edges to an undirected edge?

I have a directed graph, which for some pairs of vertices, has a directed edge between them in each direction. I would like to replace such pairs of directed edges between the same vertices but in ...
7
votes
3answers
513 views

Nested list to graph

The following nested list can be regarded as a representation of a (tree) graph: ...
7
votes
2answers
800 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 ...
7
votes
3answers
344 views