Abstract
Abstract Purpose Complex networks seem to be ubiquitous objects in contemporary research, both in the natural and social sciences. An important area of research regarding the applicability and modeling of graph- theoretical-oriented approaches to complex systems, is the probabilistic inference of such networks. There exist different methods and algorithms designed for this purpose, most of them are inspired in statistical mechanics and rely on information theoretical grounds. An important shortcoming for most of these methods, when it comes to disentangle the actual structure of complex networks, is that they fail to distinguish between direct and indirect interactions. Here, we suggest a method to discover and assess for such indirect interactions within the framework of information theory. Methods Information-theoretical measures (in particular, Mutual Information) are applied for the probabilistic inference of complex networks. Data Processing Inequality is used to find and assess for direct and indirect interactions impact in complex networks. Results We outline the mathematical basis of information-theoretical assessment of complex network structure and discuss some examples of application in the fields of biological systems and social networks. Conclusions Information theory provides to the field of complex networks analysis with effective means for structural assessment with a computational burden low enough to be useful in both, Biological and Social network analysis.
Highlights
Complex networks, no doubt constitute one of the cornerstones of contemporary research in many branches of science (Barabási 2012; Newman 2003)
Information theory provides to the field of complex networks analysis with effective means for structural assessment with a computational burden low enough to be useful in both, Biological and Social network analysis
Network assessment in biological networks In order to introduce the need for complex network assessment of indirect interactions, let us consider the case of the gene regulatory network of the fruit fly (Drosophila melanogaster, D.m.), which is one of the best curated biological networks that has been constructed ever
Summary
No doubt constitute one of the cornerstones of contemporary research in many branches of science (Barabási 2012; Newman 2003). Alongside with the statistical analysis of large complex networks, the need for robust methodologies to infer such networks from empirical data has risen. Hernández-Lemus and Siqueiros-García Complex Adaptive Systems Modeling 2013, 1:8 http://www.casmodeling.com/content/1/1/8 large networks from noisy data sources (Bansal et al 2007; de Jong 2002; HernándezLemus et al 2009), complex network researchers in general, are confronted with some subtler structural challenges in network reconstruction. One of such challenges lies in the capacity to assess direct from indirect interactions (Chua et al 2008; Tresch et al 2007)
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