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https://github.com/mzguntalan/spring
https://github.com/mzguntalan/spring
graph graph-algorithms graphdrawing jax network
Last synced: 13 days ago
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- Host: GitHub
- URL: https://github.com/mzguntalan/spring
- Owner: mzguntalan
- Created: 2024-08-17T02:40:16.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2024-08-17T12:52:34.000Z (6 months ago)
- Last Synced: 2024-08-18T13:58:49.784Z (6 months ago)
- Topics: graph, graph-algorithms, graphdrawing, jax, network
- Language: Python
- Homepage:
- Size: 9.77 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# spring
Implementation of "Graph Drawing by Force-directed Placement" by Frutcherman and Reingold in 1991
using the jit-jax. This repo interprets the procedural/step-by-step nature of the algorithm
into a matrix and gpu-friendly manner.
This algorithm is used almost everywhere you see beautiful graph/networks like from networkx.
Most of the procedures and formulae have been merged into the equation below.
For a Graph $G = $, let $\Delta = V[None,:,:] - V[:, None,:]$ pairwise vectors from $i$ to $j$ for any $\Delta_{ij}$.
The attractive displacement is $F_A = \frac{E \Delta |\Delta|}{k}$ and the repulsive displacement is $F_R = -\frac{\Delta k^2}{ |\Delta|^2}$. And the total displament for each pairwise interactions is $D$.
$$D = \frac{E\Delta|\Delta|^3 - \Delta k^3}{k |\Delta|^2}$$
At this point $D \in \mathbb{R}^{n \times n \times 2}$ and shows the displacement contribution of each pair of nodes. $d = \Sigma_j D_j$ where $d \in \mathbb{R}^{n \times 2}$ is the raw update vector for V.
The last part of the algorithm is to cap the updates in either the $x$ or $y$ direction by the temperature $\tau$ at time $t$.
Hyperparameters of this algorithm include the number of steps, initializations, and the cooling function for determining the temperature.
## Demonstrations
The gifs take a while to start (because of recording). The speed is intentionally slow for demonstration.
