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Structural changes in a network representation of a system (e.g.,different experimental conditions, time evolution), can provide insight on its organization, function and on how it responds to external perturbations. The deeper understanding of how gene networks cope with diseases and treatments is maybe the most incisive demonstration of the gains obtained through this differential network analysis point-of-view, which lead to an explosion of new numeric techniques in the last decade. However, {it where} to focus ones attention, or how to navigate through the differential structures can be overwhelming even for few experimental conditions. In this paper, we propose a theory and a methodological implementation for the characterization of shared structural roles of nodes simultaneously within and between networks, whose outcome is a highly {em interpretable} map. The main features and accuracy are investigated with numerical benchmarks generated by a stochastic block model. Results show that it can provide nuanced and interpretable information in scenarios with very different (i) community sizes and (ii) total number of communities, and (iii) even for a large number of 100 networks been compared (e.g., for 100 different experimental conditions). Then, we show evidence that the strength of the method is its story-telling-like characterization of the information encoded in a set of networks, which can be used to pinpoint unexpected differential structures, leading to further investigations and providing new insights. We provide an illustrative, exploratory analysis of four gene co-expression networks from two cell types $times$ two treatments (interferon-$beta$ stimulated or control). The method proposed here allowed us to elaborate and test a set of very specific hypotheses related to {em unique} and {em subtle} nuances of the structural differences between these networks.
In a network, we define shell $ell$ as the set of nodes at distance $ell$ with respect to a given node and define $r_ell$ as the fraction of nodes outside shell $ell$. In a transport process, information or disease usually diffuses from a random node
Much recent empirical evidence shows that textit{community structure} is ubiquitous in the real-world networks. In this Letter, we propose a growth model to create scale-free networks with the tunable strength (noted by $Q$) of community structure an
We present a new benchmarking procedure that is unambiguous and specific to local community-finding methods, allowing one to compare the accuracy of various methods. We apply this to new and existing algorithms. A simple class of synthetic benchmark
Many complex systems, including networks, are not static but can display strong fluctuations at various time scales. Characterizing the dynamics in complex networks is thus of the utmost importance in the understanding of these networks and of the dy
The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based on their