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

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13
votes
4answers
468 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 ...
13
votes
1answer
416 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. ...
12
votes
2answers
1k 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 ...
12
votes
4answers
1k 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 ...
12
votes
2answers
515 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 ...
12
votes
2answers
358 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: ...
12
votes
1answer
200 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 ...
12
votes
1answer
1k 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: ...
12
votes
1answer
650 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 ...
12
votes
2answers
1k 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 ...
12
votes
2answers
361 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 ...
11
votes
4answers
12k 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 ...
11
votes
1answer
352 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 ...
11
votes
2answers
810 views

Combinatorica package and graph-theoretical issues

I've searched for a solution to my problem a couple of days, and I didn't find one. Hope you guys can help me. I'm currently trying to solve some graph-theoretical problems. One of them is to find ...
11
votes
2answers
190 views

Graph smoothing keeping vertices fixed?

Context Given a Graph like this one: ...
11
votes
1answer
345 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 ...
11
votes
2answers
531 views

Dynamic graphics are less responsive inside a Manipulate

I have some code which displays a GraphPlot and allows the user to click on any vertex in the graph to display some information about that vertex in a popup window. ...
11
votes
1answer
482 views

Drawing dessins d'enfants (bipartite graphs subject to certain conditions)

I want to write a function which constructs all possible dessins d'enfants (bipartite graphs fulfilling certain criteria, given below) from a collection of data presented in the following form: ...
10
votes
4answers
653 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 ...
10
votes
2answers
303 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
2answers
197 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
490 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
3answers
805 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
2answers
279 views

Why is NeighborhoodGraph so slow?

To get neighboring vertices I first tried: gg = GridGraph[{10, 10, 10, 10}]; VertexList[NeighborhoodGraph[gg, 1, 1]] // AbsoluteTiming {5.539308, {1, 2, 11, ...
10
votes
1answer
861 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 ...
10
votes
1answer
658 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
187 views

Issue with PathGraph

I am having a strange issue with PathGraph. Executing PathGraph[{a, b, c}] or ...
10
votes
2answers
483 views

Select a directed SubGraph without sinks and sources

Consider the following problem: Assume you have a large list of directed edges, that constitute a large graph. I would like to provide an initial subset of vertices and I need to know which additional ...
10
votes
1answer
163 views

Figuring out how AbsoluteOptions works with Graphs

I am puzzled by how AbsoluteOptions works with Graph objects. I would have expected that one could use it to obtain all the ...
9
votes
4answers
481 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
4answers
236 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
2answers
548 views

Extracting vertex coordinates from an automatically laid out graph

Given a Graph with an automatically computed layout (i.e. not explicitly given VertexCoordinates, but using a ...
9
votes
3answers
403 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
3answers
238 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 ...
9
votes
3answers
510 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 ...
9
votes
1answer
944 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 ...
9
votes
1answer
251 views

Dual graph of an arbitrary (planar) graph

Every planar graph has a dual. How can I obtain it with Mathematica? I know that GraphData provides the DualGraph property for ...
9
votes
1answer
159 views

Algorithm used by IsomorphicGraphQ

I'd like to know which algorithm is used to test if two graphs are isomorphic?
9
votes
2answers
322 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
269 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
2answers
281 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 ...
9
votes
1answer
686 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 ...
9
votes
1answer
326 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
2answers
1k views

Mathematica Package for Bayesian Networks

Are there any packages that allow the simulation of Bayesian Networks with Mathematica? I found what seemed to be a promising package (Dynamics) on a Brown University URL, ...
9
votes
4answers
286 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. ...
9
votes
1answer
376 views

Drawing Zonotopes from Adjacency Matrix

This is crossposted in cs.stackexchange.com, but I have been trying to use Mathematica do this and figured it might be more appropriate to ask here. Define a "simple zonotope" to be a regular ...
9
votes
1answer
130 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
1answer
110 views

FindHamiltonianCycle is not invariant to edge permutation

Found this bug-like behaviour today: if the order of edges is changed so that VertexList does not return the vertices in canonical order, ...
9
votes
1answer
199 views

Binary decision diagrams (BDD)

I would like to use Mathematica to help me simplify a given Binary Decision Diagram (i.e. pick the optimal variable ordering). I don't seem to find anything at all on the topic, although it is ...
8
votes
3answers
490 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 ...