Abstract
Many complex systems present an intrinsic bipartite nature and are described and modeled in terms of networks. Bipartite networks are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set and the heterogeneity makes it very difficult to discriminate preferential links between the elements from randomly occurring links reflecting system heterogeneity. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis, which takes into account system heterogeneity. We apply our method to a biological, an economic and a social complex system. Our method is able to detect network structures which are informative about the organization and specialization of the investigated systems. Specifically, our method (i) identifies the preferential relationships between the elements, (ii) highlights the clustered structure of systems, and (iii) defines and classifies links according to the type of statistically validated relationships between the connected nodes.
Highlights
In recent years, many complex systems have been described and modeled in terms of bipartite networks [1,2,3,4,5]
Bipartite networks are composed by two different sets of nodes such that every link connects a node of the first set with a node of the second set
A projected network of organisms based on the co-occurrence of specific clusters of orthologous genes (COG) might highlight the degree of similarity of two organisms based on the functional characteristics of proteins present in their genome
Summary
Many complex systems have been described and modeled in terms of bipartite networks [1,2,3,4,5]. One ubiquitous property of bipartite complex systems is their heterogeneity. In a given period of time, some actors play in many movies, whereas others play in a few, some authors write a few papers, whereas others write many. Movies are heterogeneous because of the size of cast, as well as papers because of the number of authors. Heterogeneity is a common feature of biological complex systems. Bipartite networks are composed by two different sets of nodes such that every link connects a node of the first set with a node of the second set. The properties of bipartite complex systems are often investigated by considering the one-mode projection of the bipartite network. One creates a network of nodes belonging to one of the two sets and two nodes are connected when they have at least one common neighboring node of the other set. In this paper we deal with the problem of identifying preferential links in the projected network
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