# Lin Log Model

The clustering mechanism used here is the Ling Log model. The Lin Log model was an energy algorithm designed by Andreas Noack to provide an efficient way to minimize the energy in our force-directed cluster graph. It is this algorithm that we implemented in the creation of our java program. Like all energy models, the Lin Log model has two parts: an energy model and an algorithm to iterate to find the lowest energy. The model is based on the idea that the lowest energy is achieved by minimizing the ratio between the average edge length to average distance to all nodes. It provides the minimal ration of the arithmetic mean of the edges to the geometrical mean of node distances. With each point p, the algorithm aims to achieve for a set a constant c, p’ = c/(|E| arithmeticmean(E, p))*p where E is the edgelength. The LinLog model establishes the cut ratio as the fraction of possible edges between one node and another node. Cutratio(V1, V2) = |E[V1, V2]|/(|V1| · |V2|). Then, the Lin Log model proposes the idea that wherever one cuts a one-dimensional minimum LinLog energy drawing into two nonempty parts, the harmonic mean of the distances between the nodes in the two parts equals the inverse cut ratio.