Figure 1

Illustration of the fuzzy clustering approach. We want to approximate the tripartite example graph G in (a) by a smaller tripartite cluster network H, the so-called backbone graph (b). The decomposition into fuzzy clusters connected by this backbone must explain the original connectivity as good as possible. The edges of G are collected in adjacency matrices A^(ij)connecting the elements of the partitions i and j. The approximation of G by the backbone graph is encoded in the adjacency matrices B^(ij)connecting the fuzzy node clusters C⁽ⁱ⁾. These matrices C⁽ⁱ⁾collect the degrees of membership of each node of partition V _i to each cluster of this type. Its (k, l)-th element $C_{kl}^{(i)}$ specifies how much node k belongs to the backbone node l.