hyperrogue/rogueviz/sag

What is it

The SAG module is used to create the embeddings of graphs, and to render them.

In general, this works by mapping the nodes of a graph to the cells of a RogueViz-supported tessellation or honeycomb. The number of usable cells is limited (that is, a fixed region is set in advance for the embedding).

Simulated Annealing is used to find the 'optimal' mapping. The function optimized depends on the method. Currently, there are three main 'methods' implemented:

NEAREST: we minimize the sum of w * d over all edges, where w is the edge weight, and d is the distance between the endpoints of that edge. In other words, we want to place all nodes all close as possible, especially if the node weights are big. See the following visualizations as an example of visualizations obtained using this method:

https://www.youtube.com/watch?v=mDG3_f8R2Ns (SAG boardgames) https://www.youtube.com/watch?v=WSyygk_3j9o (SAG roguelikes) https://www.youtube.com/watch?v=HWQkDkeEUeM (SAG programming languages)

MATCH: we minimize the sum of squares of (d - a/w - b), where w and d are as above. In other words, we want the distance between nodes to represent 1/w as well as possible; a and b are scaling parameters.

(no examples for now)

LIKELIHOOD: this method is based on the Hyperbolic Random Graph model. According to that model, each pair of nodes in distance d are connected with probability 1/(1+\exp((d-R)/T)). We maximize the likelihood, i.e., the product of these probabilities for actual edges, and their complements for non-edges. In other words, nodes connected with edges want to be close, while nodes not connected with edges want to be distant.

The following embeddings have been obtained using this method:

https://youtu.be/GQKaKF_yOL4 (brain connectomes)

The rest of this README details how to use SAG.

Cells

Not yet documented

Graph

Just use -sag-weighted to read a weighted graph (in format node1;node2;weight), or -sag-unweighted to read an unweighted graph (in format node1 node2).