# Questions tagged [graphs-and-networks]

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

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### How Color the PathGraph Showing Multiple Shortest Paths on the US Counties Map

Below is code for mapping the connectivity of US counties. It comes from the Mathematica reference on "Connectivity of US Counties". I've highlighted 3 shortest paths shown in red. However, ...
27 views

### SpatialGraphDistribution with DirectedEdges` doesn't work

I want to create a random graph with SpatialDegreeDistribution and want the edges to be directed. ...
49 views

### Drawing graphs with many vertices in mathematica [duplicate]

I have been using Mathematica to make graphs out of adjacency matrices. However, once the adjacency matrices get very large, Mathematica does not draw them. My adjacency matrix is a 360x360 matrix. Is ...
24 views

### Extracting GraphDistance out of SpatialGraphDistribution

I am trying to generate a graph which has Euclidean distances between the vertices. The documentation for SpatialGraphDistribution says that ...
34 views

### How can I find average clustering coefficient in an undirected Erdos–Rényi graph? [closed]

My question is: What is the average clustering coefficient in an undirected Erdos–Rényi graph with N = 10 nodes and M = 18 links? Here just I have to find p? p is the answer or c=K/N is the answer? L=...
143 views
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### How to Breakout Edge Betweenness Centrality

Consider the following: ...
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### FindCycle with EdgeWeight in directed graphs

Following up on the discussion in Problem with EdgeWeight and FindCycle?, consider the simple directed graph: ...
64 views

### How to create a representation of a multilayered neural network from scratch using Graph?

One valid way is given at the end. I thought CompleteGraph[{2, 3, 3, 1}] would create the representation that I wanted but it creates too many edges (from the first ...
65 views

### Can one hide the vertex of a graph or create an edge that passes through a specific point in the underlying coordinate space?

If one creates a graph with two edges between the same two vertices, WL draws them in a default coordinate space in which the two edges that pass-through coordinate positions that are placed on curved ...
84 views

### How to link a variable to vertices of a directed graph using bubles with different sizes

This Code produces a directed graph: ...
100 views

### Dense packing of disks with different radii

Let's consider a disk ($D_{1}$) whose center position is randomly generated, but the radius is fixed at $r_{1}$. A second disk ($D_{2}$) of fixed radius $r_{2}$ (with $r_{2} < r_{1}$) is randomly ...
81 views

### Finding a mapping between two graphs

I am trying to find a function / algorithm that will search and find a mapping between an irregular graph (say, N-nodes with maximum vertex degree-K but otherwise irregular) into a regular L-nearest ...
220 views

### How to plot a signal (function) on a graph (object of graph theory)

Given a graph of n vertices, it is possible to plot a discrete signal (or function) of n samples on the vertices of the graph, so that one can visualize the features of the signal on the graph (see ...
89 views

### Why does Mathematica not display networks? [duplicate]

Why does Mathematica not display (and export) the graph 'g' when n> 10000? n = 10000; g = RandomGraph[BarabasiAlbertGraphDistribution[n, 1]] ralph
64 views

### Representing and Extracting Properties of a System Product Breakdown Structure (a Directed Acyclic Graph)

I am trying to analyze products using a product breakdown structure (PBS), which is a directed acyclic graph (DAG) that reflects a decomposition of the product into subproducts, sub-sub-products, and ...
74 views

### How can one calculate the co-normal (disjunctive/or) product of two graphs in Wolfram Language?

I'm trying to verify a result in Wolfram Cloud. The standard cartesian graph product is implemented. Graph join is implemented. But it seems that the co-normal product does not seem to be, and ...
74 views

### How to get neighbor lists in the same order/orientation from a periodic IGTriangularLattice[] graph?

Using IGraphM, I want to get the VertexComponent[] neighbors around all nodes, in a periodic IGTriangularLattice[] graph. To do ...
128 views

### Determine Level Structure of Graph

I am trying to output the level structure of a graph (for example, a graph with edges {{1,2},{2,3},{3,4},{3,5},{3,6},{4,7}} would have a level structure {1: {1}, 2: {2}, 3: {3}, 4: {4, 5, 6}, 5: {7}})....
68 views

### Rename a Graph Vertex [closed]

We have VertexAdd, VertexDelete, EdgeAdd, EdgeDelete but no VertexRename. Is there a simple way to achieve this? I fiddled around with AnnotationValue,AnnotationKeys,IndicedenceList etc to create a ...
51 views

### IGMotifsVertexParticipation Problem

I have a directed acyclic graph with 194 vertices and 492 edges. I was able to get the 3-motifs without a problem. However, when I ran IGMotifsVertexParticipation I got an error message. I ran the ...
48 views

### Visulisation of k-core decomposition complex network

How can I visualize a complex network in the way it is presented in Fig. 4 the following article: https://proceedings.neurips.cc/paper/2005/file/b19aa25ff58940d974234b48391b9549-Paper.pdf ? I have ...
194 views

### Compute a subdivision graph

I'm trying to compute a subdivision graph of an arbitrary graph by adding one vertex in the middle of each edge of the graph.
164 views

### FindPath with required Edges

Suppose I have a graph g with some edges reqEdges (in the example code here, just one edge). I would like to use ...
211 views

### How to find all possible paths between a collection of vertices in a DAG graph

I have a toy example "system" that is a DAG and has 16 vertices. Suppose I have a collection of vertices "collection". How can I find all paths that passes through at least all ...
65 views

### VertexInComponent not working properly on edgless graphs

Bug introduced in 12.1 and persisting through 12.3.1 Note: The 3rd argument of VertexInComponent was introduced in 12.1. The code ...
56 views

### FindCycle Evaluation Time Diverges

I have a data set of 257,182 edges between 32,849 vertices forming a directed graph. I would like to use FindCycle to analyse its cycle structure. Unsurprisingly, ...
29 views

The code: ...
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### Is there a way to make FindSpanningTree return a directed graph?

I would like to use edge-direction to distinguish between parents and children in a given spanning tree. When choice of root-node is not unique FindSpanningTree ...
63 views

### Efficient way to get all $k$-factors of a graph $G$?

In Graph factorization, a $k$-factor of a graph $G$ is a spanning $k$-regular subgraph which has the same vertex set as $G$. Now I have a random graph $g$ (i.e. complete graph for simplicity) and I ...
193 views

### Plotting of probability density on a lattice and studying dynamics

I have a lattice described by a AdjacencyMatrix or Hamiltonian. This matrix has all the information of how each site is connected to another site with what hopping ...
102 views

### Make Graphs with disjoint edge sets that have different colors?

I would like to obtain the related graphs in mathematica which look like the following picture took from this link: What I do: I have all the edge lists for the above graphs. ...
67 views

### According to the path, how to draw such a binary tree?

As shown in the figure, the path can be generated by the following code ...
40 views

### How to creat a high-quality graph image for MorphologicalGraph to convert to graphs (it can't detect some edges in mine)?

I'm using MorphologicalGraph to convert images to graph. This is my source image: Following this and this, I tried ...
146 views

### Connecting simple lines from (large) unsorted list of points

Context We are trying to predict the formation of discs of intermediate mass black hole orbiting super massive black holes in galactic centres. This involves finding calorific curves in energy and ...
386 views

### Arbitrary lattice graph in 2D

My purpose is to generate a graph representing a lattice, where the vertices are essentially the lattice sites. This lattice has to be periodic. That means the opposite boundaries are identical. MWE ...
37 views

### Different codes give different star embedding graph layout

I usually use the following code to generate a star embedding graph layout. ...
94 views

### Efficient way to pick up pairwise vertices of certain Euclidean distance in arbitrarily dimensional coordinates? [closed]

I have a grid graph with x and y vertices in each direction. The 2-dimensional coordinates of the graph ...
109 views

### How to get Gallai-Edmonds decomposition of a graph?

In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into subsets satisfying certain properties. Describe it in more detail. from here To get the maximum ...
68 views

### How to calculate and display possible graphs from 3 directed branches?

I have 3 directed branches and I want to create all possible graphs that can be created from these branches with the condition that each branch is used once. Q1: How can I do create and graph them? ...
333 views

### Generate Hexagon within Hexagon and show only certain connections

How can I generate the hexagons shown? I'd like to add names to all the disks and the colored links. And rotate the whole thing by 30 degrees.
91 views

### How to display all graph layouts at once?

I often find myself manually trying different graph layouts (Radial Drawing, Layered Drawing, etc ...) to find the best possible visualization for graphs. Is there a quick command to display ALL graph ...
59 views

### Retain Edge Ordering in DAG Conversion

I would like to convert an undirected graph into a directed graph such that for each tuple, the first value is a head and the second is a tail in a directed edge. Initially I thought using ...
54 views

### Color-code edges by order in edge list

Given a graph with vertex coordinates list V and edge list E, how can I visualize the order of appearance of edges in E? It is similar to this and this question which ask how to color-code points in a ...
236 views

### Improving label collisions for Tree/Graph?

Historically, MMA has never handled label collisions well, but recently they added some improvements here via things like Callout. I want to fix ImageSize but still ...
289 views

### Generate Aztec triangle of size n automatically？

In the paper titled "Perfect Matchings of Cellular Graphs" by Mihai Ciucu, the Aztec triangle of size n (n= 1, 2, 3, 4, 5, ...) is equivalent to a ...
59 views

### How to mark nodes and insert weights in an adjacency graph?

I have a graph with 12 nodes. The x and y coordinates are give as ...
57 views

### Output vertex pair(s) whose distance is the graph's diameter

Assuming you have a connected graph (in my case also undirected and equal/no edge weights), how could you see all the vertex pairs whose shortest length path is equal to the graph's diameter? An ...
48 views

### How to represent a subgraph of a directed graph as a LayeredGraph with EdgeWeights

The following code generates: The first element is a layered graph of the original system sam. The second element is a list of ...