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

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5
votes
2answers
196 views

Is there something wrong with VertexConnectivity

As I noticed in the documentation VertexConnectivity is defined as the following The vertex connectivity of a graph $g$ is the smallest number of vertices whose ...
21
votes
3answers
2k 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 ...
18
votes
1answer
382 views

How to visualize large graphs with directed edge bundling

I'm wondering if anyone has implemented edge bundled graph plotting? http://www.win.tue.nl/~dholten/papers/forcebundles_eurovis.pdf
14
votes
2answers
593 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: ...
14
votes
3answers
992 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 ...
14
votes
2answers
531 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 ...
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 ...
11
votes
1answer
313 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 ...
10
votes
1answer
506 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 ...
16
votes
3answers
427 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 ...
13
votes
3answers
603 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 ...
15
votes
3answers
225 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: ...
13
votes
2answers
923 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 ...
12
votes
2answers
476 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 ...
7
votes
4answers
305 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 ...
20
votes
1answer
803 views

Graph vs GraphPlot

What is the difference (in purpose) between Graph and GraphPlot? Which function is bested suited to which tasks? Background: I ...
17
votes
2answers
357 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 ...
13
votes
4answers
429 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 ...
6
votes
1answer
291 views

How to visualize the structure of this dynamic programming code

I am studying Mr. Wizard's answer to this question which tries to identify elementary circles in a graph. That answer uses dynamic programming technique to simplify the code. The underlying guideline ...
5
votes
3answers
225 views
5
votes
2answers
264 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 $G$ ...
14
votes
1answer
380 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?
12
votes
1answer
185 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 ...
9
votes
3answers
370 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
242 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
2answers
299 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 ...
8
votes
2answers
433 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 ...
6
votes
3answers
270 views

Flow in pipeline graph

I have pipeline directed graph which has one source and several sinks ...
5
votes
3answers
144 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 ...
5
votes
3answers
220 views

Nested list to graph

The following nested list can be regarded as a representation of a (tree) graph: ...
5
votes
1answer
364 views

How to display each step of an A star algorithm?

I wrote a pathfinding program: A*, which is an extension of Dijkstra. I want to see the result of each step at a time. Which function should I use? The main program is the notebook Astar, which is ...
5
votes
2answers
304 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 ...
5
votes
2answers
1k 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 ...
5
votes
3answers
983 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 ...
5
votes
1answer
207 views

How to view all graphs available in GraphData?

Is there a "gallery" view of all the graphs available in GraphData? I realize that some graphs may not lend themselves to such representation (e.g. some may have ...
5
votes
1answer
929 views

When do I use Mathematica, when do I use Gephi, and how do I use them together?

Mathematica has great operations for analyzing graphs but when the graphs are a bit bigger, Gephi seems to be more efficient (at least on my computer) at drawing and analyzing, i.e. visualizing the ...
3
votes
2answers
217 views

Showing a forest with root of the trees on the top

I have a Graph object that contains a forest with directed trees. I want to draw the forest such that the root of the trees are on the top and the leaves are on the bottom. If I use the following line ...
1
vote
2answers
316 views

EdgeRenderingFunction question

(Edit 1 : I added this paragraph after the original post, for context) Some context for this question can be found in another post (Problem with EdgeRenderingFunction), which however may be taken ...
9
votes
1answer
142 views

Algorithm used by IsomorphicGraphQ

I'd like to know which algorithm is used to test if two graphs are isomorphic?
7
votes
1answer
790 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 ...
6
votes
2answers
250 views

How to color edges of a graph which has multiple edges connecting certain vertices

I'm studying BIBD(Balanced Incomplete Block Design) and want to draw some graphs by coloring their blocks in different colors, respectively. A block is a collection of edges (or vertices). For ...
6
votes
1answer
136 views

Property assignment on a graph vertex using PropertyValue does not work inside a function

I created this function: AddStone[board_Graph, v_, s : white | black | empty] := PropertyValue[{board, v}, VertexState] = s This function should change the ...
6
votes
2answers
226 views

Truncate TreeForm to show only the top

For some expressions, TreeForm may grow very long. I'm only interested in the top levels of the expression. How can I get the tree form of only the first levels an ...
5
votes
1answer
470 views

How can I draw a polygon from a set of angles?

In recreational mathematics, polytans are polygons formed by edge-connecting isosceles right triangles. Order-n polytans are those constructed from n such triangles. My question is this: Given a ...
4
votes
1answer
331 views

Analysis of Facebook group

I am the admin of a Facebook group for our year at university and wanted to graph the members of the group like you can with your own friends so we can find the isolated people and get rid of them (as ...
4
votes
2answers
241 views

Efficiently determining the largest minimum cost to travel from a fixed source to an arbitrary sink in a weighted graph

Let $v_i$ be a vertex in a graph $G$ with vertices $(v_1,...,v_N) \in V$ and edges $(e_1,...,e_M) \in E$ with associated weights $(w_1,...,w_M)$. Let $v_s \in V$ be specified vertex in the graph. In ...
3
votes
3answers
272 views

Generating a graph where vertices correspond to points in an integer lattice and edges connect points less than a threshold distance apart

I'd like to automatically generate a graph where vertices correspond to (and have the coordinates of) points in an $A \times B$ integer lattice, and a graph is generated by connected vertices within a ...
0
votes
1answer
131 views

Display a labeled multigraph

Despite the integration of graphs and networks, multigraphs are not supported in Mathematica 8+. In Mathematica 9+, GraphPlot misbehaves for multigraphs having ...
8
votes
3answers
404 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: ...
7
votes
1answer
214 views

Making FindShortestPath a little bit sloppy [duplicate]

I have a dense graph, and I'd like to find multiple "almost shortest" paths from a source vertex, $v_s$, to a sink vertex, $v_s$, on an undirected graph $G$. How can I repeatedly run ...