# Tagged Questions

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

321 views

### Citation of the algorithms used in FindGraphCommunities

For my research work I need to put a comparison of different community detection algorithms. Instead of implementing all those algorithms once again, I would like to use the methods already provided ...
283 views

### Coordinate extraction and manipulating graphs as graphics objects

Consider the image below: GraphData[{"Wheel", 7}] Is it possible in Mathematica to lay several of these Graph along each ...
69 views

### Importing additional custom data in DIMACS format

I have graphs in DIMACS format, with vertex colors specified. The vertex colors are denoted by lines n u c, where u is the ...
708 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 that'...
127 views

### Using FindGraphCommunities, write community membership for each vertex to CSV

I have a network that I've loaded into Mathematica, and I've used FindGraphCommunitites[network,Method->"Hierarchical"] to identify the communities in the ...
141 views

### Expected graph distance in random graph

I am trying to use the functionality of Expectation and Probability for random graphs, in particular for percolation models. ...
647 views

### Positioning Vertices in a Graph

I made a graph that has a given number at each vertex: I want to place vertex 1 above vertex 2 if value of vertex 1 is larger than of vertex 2. And also, vertices with same value should be located ...
173 views

### Fix the size of vertices and arrow in graphs

I defined an option to draw nicely the graph. But I have a problem with the different size obtained. For example, the layout of the first graph is what I want to have for all other graphs I will ...
81 views

### What Algorithm Does Mathematica use to Calculate Betweenness Centrality for Unweighted Graphs?

I recently asked this question on the Mathematics SE. Does anyone know, as a follow up, what algorithm Mathematica uses to calculate the betweenness centrality vector (of $N$ elements) for an ...
498 views

### How to get all leaves from a graph's specific node

Let's say I have this graph (The code to generate the graph is at the end) How can I extract all the leaves comming from, let's say "cluster3"?, i.e. {100, 92, 87, 89} I guess I have to first ...
105 views

### Graph plotting: specify layers for layered drawing

Mathematica can do layered graph drawing with LayeredGraphPlot or GraphLayout -> "LayeredEmbedding". Is it possible to ...
567 views

### Mathematica 10 Graph issue

Bug introduced in 10.0.0 and fixed in 10.0.2 Please try to evaluate this code in Mathematica 10. ...
201 views

### Undirected Network and its Monte Carlo Simulation

So I have this array of points, in the form {x, {y,z}}, where x is the node number assigned when I used the locator pane to make a network, and y and z are its unitary coordinates. The graph is made ...
157 views

### Agglomerate output to Graph

I'm using the HierarchicalClustering package to cluster some data. So let's say I have this: ...
215 views

### Systemic bugs in GraphPlot and related functions such as TreePlot and TreeForm

Bug introduced in 7.0.1 or earlier and fixed in 10.3.0 I believe I have come across a rather curious bug in TreeForm: ...
256 views

### Cellular Automata Neighborhood as Node connections

Can I use the CellularAutomation[] function where the neighborhood is defined by the connections between nodes? For example, if 1 -> 2, 1 -> 3, 1 -> 8, 1 ->1, then the neighborhood of node 1 is the ...
77 views

### Does anyone know the options for “HierarchicalEdgeBundling” in Mathematica?

I'm looking to reproduce the types of graph layout that are possible in D3 (http://bl.ocks.org/mbostock/7607999) in Mathematica. Since Mathematica doesn't explicitly support force directed edge ...
992 views

### How to plot a graph from it's incidence matrix?

I'm using Mathematica v9 and am trying to draw a graph by using it's incidence graph, but it won't draw it, which occurs an error "is not a valid incidence matrix.". But I've checked my matrix, and it'...
286 views

### Harmonious graph labeling

Is it possible to harmoniously label a graph in Mathematica? I would like a function, that when given a graph, would return a harmonious labeling. If not, is there other software that can do it? A ...
236 views

### Hungarian Algorithm using BipartiteMatchingAndCover Function

I have a bipartite graph with two sets of vertices. ...
288 views

### How to construct a polyhedron from its vertex graph?

Consider the graph given by ...
384 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 ...
440 views

### How to draw a combinatorial graph with different colors of edges?

For example, like above. I've read some examples and descriptions in here, but couldn't figured it out.
79 views

### Make AdjacencyGraph hide single unconnected elements

Is there a way to force AdjacencyGraph to hide single unconnected or self connected elements? ...
593 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 ...
211 views

### Generate Random 3D Network using GraphPlot3D and loop

Instead of writing all this out I want to do the same thing with a loop and be able to manipulate n and k. The idea is to create a randomly generated network where n is the number of nodes and k is ...
193 views

### Creating a Network from a Output

So I used the locator pane to derive the positions of a vertex on a picture. The picture was the Maryland Power Grid and the vertices were the generators and loads of the power system. When I clicked ...
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 ...
743 views

### How to find a path that traverses each edge of a graph exactly twice?

I have a question regarding a graph traversal problem. This is the graph I am working with: ...
142 views

### How can I speed up the export of graphs in DIMACS format?

I'm creating random graphs with suitable properties and exporting them in the DIMACS format. Already, for rather small graphs with, say, ~60k vertices and ~240k edges, ...
207 views

### How to obtain all the distinct De Bruijn sequences?

In combinatorial mathematics, a $k$-ary De Bruijn sequence $B(k, n)$ of order $n$ is a cyclic sequence of a given alphabet $A$ with size $k$ for which every possible subsequence of length $n$ in $A$ ...
202 views

### Why the Mouse dragging response not as smooth as Locator

I am experimenting to use MouseDragged eventhandler to change the vertices positions of a triangle, it works, but not as smooth as using Locators. Is this the ...
149 views

### The algorithm of ListGraphs[n,m]

I'm not sure if this is a Mathematica problem, math problem or a CS problem, so if this is off-topic please transfer it. In the package Combinatorica there is a ...
148 views

### Vertex Names of Subgraph in Order of Connectivity

I extract path subgraphs $P_4$ of an undirected graph $G$. And want to list the VertexNames of the subgraphs in the same order as they are connected. Here is an example: ...
2k views

### Longest path in 0/1 matrix

I have a matrix of 0's and 1's forming a number of disjoint paths:   I would like to find the lengths of the paths, and from that "spectrum," the longest length (in the above example: 27, ...
368 views

### Map of all graphs obtainable with GraphData?

I've been trying to put together an answer to another question, but I am stuck, so I decided to post this question instead. Mathematica contains (among its curated data) information on definition, ...
252 views

### How to generate a random binary tree with a given number of vertices and with a given shape, namely compact or elongated

I tried to generate a random binary tree with a Table of RandomInteger and to give a shape with a ...
195 views

### Sequence of binary trees with different source nodes and with the same Strahler hierarchical order

I would like to create a picture which contains a sequence of binary trees with the same Strahler hierarchical order (for example equal to 2) e with a sequence of different source nodes "i" (from 1 to ...
100 views

### Rendering of a HighlightGraph in a Manipulate content pane distorted by changing the highlighted edge

A HighlightGraph inside a Manipulate initially displays correct however after approximately 2 seconds, the layout changes and ...
183 views

### Labeling vertices by number in Graph: Getting text to display at the right size

Minor aesthetic question here. I was playing around with Graph's and decided to render a cute-looking family of directed graphs, with the vertices being the number ...
112 views

### Using CombinatoricaListNecklaces in v9

I am using Mathematica for visualization of DeBruijn graphs. However, I am having a bit of trouble using ListNecklaces. I want to know how many cyclic shifts of ...
288 views

### Understanding performance: graph connected components

I need to analyze directed graphs with 10M edges, 1M vertices, and 300K strongly connected components, so that the largest one contains 400K vertices. I read some explanations of Leonid Shifrin here, ...
110 views

### Centrality measures and normalisation

Are centrality measures normalised in Mathematica 9? Only ClosenessCentrality is normalised. How I can normalise other centrality measures notably ...
145 views

### distance between each vertex of a graph and its output

I have a question regarding this Q&A. Let's call a vertex that is not the tail of any directed edge an output of the graph. The graph below has only one output (at the far right). If I want the ...
431 views

### Triangular lattice with periodic boundary conditions

I am trying to generate an equilateral triangular lattice with fixed vertices and periodic boundary conditions. I am supposed to assign an index (starting from 0) to each vertex in my lattice and then ...
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 ...
539 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 ...
62 views

The code ...