Which algorithm(s) for which representation ?

The Logic of "Force-Based" Layouts

Nodes repel each other like magnets, while links pull the nodes they connect together, like springs.

These forces set the nodes in motion until a point of equilibrium is reached (where the nodes stop moving).

Highlighting Divisions Between Different Components of the Map

OpenOrd aims to emphasize divisions between the various parts of the map.

Highlighting Complementarities Between Different Elements of the Map

📘 Force Atlas Algorithm

Force Atlas is designed to spatialize small-world/scale-free networks. It focuses on quality to explore "real data" and enable rigorous interpretation of the graph with minimal bias and good readability.

The repulsion force depends on the density of nodes and their relationships, with the goal of clearly distinguishing nodes and making each label readable (displayed via the "T" at the bottom of the screen). The size adjustment variable helps avoid overlaps.

• Works with 1 to 10,000 nodes. Allows highlighting the weight of nodes.

Notably, "Force Atlas 2" is available, an adapted version of the algorithm for handling networks with several hundred thousand nodes.

📘 Fruchterman-Reingold Algorithm

Fruchterman-Reingold is the classic layout. Forces act between neighboring nodes, simulating the graph as a system of mass particles. Nodes are the mass particles, and edges act as springs between them.

• Works with 1 to 1,000 nodes. No node weighting.

📘 Kamada and Kawai Algorithm

The Kamada and Kawai algorithm uses an attraction force between two nodes, proportional to the shortest path length separating them.

📘 Yifan Hu Algorithm

Yifan Hu groups nodes into clusters and applies a force-based logic to these clusters. It is a very fast algorithm with high quality for large graphs. It combines a force-directed model with a coarsening technique (multi-level algorithm) to reduce complexity. Repulsion forces on a node within a cluster of distant nodes are approximated using a Barnes-Hut calculation, treating them as a super-node.

• Works with 100 to 100,000 nodes. No node weighting.

Highlighting a Classification Logic for Graph Elements

📘 Circular Axis The Circular Axis layout arranges nodes in a circle, ordered by ID, a metric (e.g., degree, betweenness centrality), or an attribute. This layout is useful for displaying a distribution of nodes along with their links.

📘 Radial Axis Layout The Radial Axis Layout groups nodes and positions the groups along axes radiating outward from a central circle. Groups are generated using a metric (e.g., degree, betweenness centrality) or an attribute. This layout is useful for studying proximities by showing the distribution of nodes within groups along with their links.

• Handles 1 to 1,000,000 nodes.

📘 GeoLayout GeoLayout provides a geographic distribution of nodes on a map base. It uses latitude/longitude coordinates to position nodes within the network. Several map projections are available, including Mercator, which is used by Google Maps and other online services. The two node attribute columns for coordinates must be in numeric format.

Other Algorithms

• Label adjustment/NoOverlap: prevents node names from overlapping on your network.

• Contraction/Expansion: increases or decreases the spacing between nodes.