Modularity and community detection in bipartite networks

The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity. The bipartite modularity is presented in terms of a modularity matrix B; some key properties of the eigenspectrum of B are identified and used to describe an algorithm for identifying modules in bipartite networks. The algorithm is based on the idea that the modules in the two parts of the network are dependent, with each part mutually being used to induce the vertices for the other part into the modules. We apply the algorithm to real-world network data, showing that the algorithm successfully identifies the modular structure of bipartite networks.Comment: RevTex 4, 11 pages, 3 figures, 1 table; modest extensions to conten

Module identification in bipartite and directed networks

Modularity is one of the most prominent properties of real-world complex networks. Here, we address the issue of module identification in two important classes of networks: bipartite networks and directed unipartite networks. Nodes in bipartite networks are divided into two non-overlapping sets, and the links must have one end node from each set. Directed unipartite networks only have one type of nodes, but links have an origin and an end. We show that directed unipartite networks can be conviniently represented as bipartite networks for module identification purposes. We report a novel approach especially suited for module detection in bipartite networks, and define a set of random networks that enable us to validate the new approach

Bias estimation in sensor networks

This paper investigates the problem of estimating biases affecting relative state measurements in a sensor network. Each sensor measures the relative states of its neighbors and this measurement is corrupted by a constant bias. We analyse under what conditions on the network topology and the maximum number of biased sensors the biases can be correctly estimated. We show that for non-bipartite graphs the biases can always be determined even when all the sensors are corrupted, while for bipartite graphs more than half of the sensors should be unbiased to ensure the correctness of the bias estimation. If the biases are heterogeneous, then the number of unbiased sensors can be reduced to two. Based on these conditions, we propose some algorithms to estimate the biases.Comment: 12 pages, 8 figure