📂Graph Theory

Mathematical Graph Layouts

Overview

In mathematics, a layout of a graph or network can be summarized as an algorithm that dictates how vertices and edges are arranged when visualized in 2D or 3D.

Code

For convenience, all code is written based on Julia which is publicly available on GitHub¹. The example graph used is generated by the Barabási-Albert model.

julia> G = barabasi_albert(50, 2)
{50, 96} undirected simple Int64 graph

julia> coordinates = random_layout(G)
([0.5010198458212828, 0.3452510059580436, 0.23056277180207596, 0.9451881326291259, 0.449381314574683, 0.4542317082538514, 0.599934409205972, 0.30717602583409154, 0.49093984675628266, 0.2715011111637651  …  0.681936012233088, 0.5814119530837815, 0.4207410774873547, 0.9727858272079993, 0.8552495989245602, 0.01141962455772294, 0.2899567788836197, 0.3666521897515005, 0.3711803454000888, 0.9162070908084106], [0.6301320613076998, 0.08213345094706803, 0.8807313434091223, 0.3037072145751386, 0.2696238790669454, 0.6634585165568677, 0.5096441313648647, 0.9252054034990449, 0.7087281373799236, 0.2122981806086709  …  0.5749195632507926, 0.7426568432084615, 0.42337991561728805, 0.7403457672559728, 0.09122908201258395, 0.06875442916534202, 0.5150784327498186, 0.0052746330721339385, 0.49087546999990384, 0.9942182342312704])

The _layout series of functions return the coordinates calculated by the algorithm. Being able to directly obtain such coordinates for visualization is a significant advantage.

spring layout

random layout

circular layout

There is also a function called shell_layout, but it has been omitted here since, despite clear implementation differences from circular_layout, there appears to be no visual distinction.

stressmajorize layout

spectral layout

Complete Code

using Graphs, GraphPlot, Plots, Random, GraphRecipes
G = barabasi_albert(50, 2)
coordinates = random_layout(G)

gplot(G, layout = spring_layout)
gplot(G, layout = random_layout)
gplot(G, layout = circular_layout)
gplot(G, layout = shell_layout)
gplot(G, layout = stressmajorize_layout)
gplot(G, layout = spectral_layout)

Environment

• OS: Windows
• julia: v1.10.0