Kamada-Kawai Force Directed Layout

• Compute layout for simple (no loops, no multiedges) undirected networks (makes directed edges undirected).
• The geometric distance between pairs of nodes should reflect the graph-theoretic distance (shortest path length) between them. Kamada-Kawai wrote: We regard the desirable geometric (Euclidean) distance between two vertices in the drawing as the graph theoretic distance between them in the corresponding graph.
• The layout uses a spring model, where for each pair of nodes a spring is defined with an ideal length proportional to the graph-theoretic distance between the nodes, and a stiffness inversely proportional to the inverse of the square of the graph-theoretic distance.
• We compute the layout by simulating a spring system with a damping term to reach a steady state. The integration is done with Verlet integration, which is a symplectic integrator that is more stable than Euler integration.

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