Robustness and modular structure in networks

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a percolation problem [7-9] or by modeling cascading failures [10-12]. Many complex systems, from power grids and the Internet to the brain and society [13-15], can be modeled using modular networks comprised of small, densely connected groups of nodes [16, 17]. These modules often overlap, with network elements belonging to multiple modules [18, 19]. Yet existing work on robustness has not considered the role of overlapping, modular structure. Here we study the robustness of these systems to the failure of elements. We show analytically and empirically that it is possible for the modules themselves to become uncoupled or non-overlapping well before the network disintegrates. If overlapping modular organization plays a role in overall functionality, networks may be far more vulnerable than predicted by conventional percolation theory.Comment: 14 pages, 9 figure

Modular networks emerge from multiconstraint optimization

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing robustness against perturbations in node activity. We show that the optimal networks satisfying these three constraints are characterized by the existence of multiple subnetworks (modules) sparsely connected to each other. In addition, these modules have distinct hubs, resulting in an overall heterogeneous degree distribution.Comment: 5 pages, 4 figures; Published versio

Hierarchical mutual information for the comparison of hierarchical community structures in complex networks

The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the {\it hierarchical mutual information}, which is a generalization of the traditional mutual information, and allows to compare hierarchical partitions and hierarchical community structures. The {\it normalized} version of the hierarchical mutual information should behave analogously to the traditional normalized mutual information. Here, the correct behavior of the hierarchical mutual information is corroborated on an extensive battery of numerical experiments. The experiments are performed on artificial hierarchies, and on the hierarchical community structure of artificial and empirical networks. Furthermore, the experiments illustrate some of the practical applications of the hierarchical mutual information. Namely, the comparison of different community detection methods, and the study of the consistency, robustness and temporal evolution of the hierarchical modular structure of networks.Comment: 14 pages and 12 figure

Interactions between tick and transmitted pathogens evolved to minimise competition through nested and coherent networks

Natural foci of ticks, pathogens, and vertebrate reservoirs display complex relationships that are key to the circulation of pathogens and infection dynamics through the landscape. However, knowledge of the interaction networks involved in transmission of tick-borne pathogens are limited because empirical studies are commonly incomplete or performed at small spatial scales. Here, we applied the methodology of ecological networks to quantify >14, 000 interactions among ticks, vertebrates, and pathogens in the western Palearctic. These natural networks are highly structured, modular, coherent, and nested to some degree. We found that the large number of vertebrates in the network contributes to its robustness and persistence. Its structure reduces interspecific competition and allows ample but modular circulation of transmitted pathogens among vertebrates. Accounting for domesticated hosts collapses the network'' s modular structure, linking groups of hosts that were previously unconnected and increasing the circulation of pathogens. This framework indicates that ticks and vertebrates interact along the shared environmental gradient, while pathogens are linked to groups of phylogenetically close reservoirs

Modular and Hierarchically Modular Organization of Brain Networks

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data

Long-range connections and mixed diffusion in fractional networks

Networks with long-range connections, obeying a distance-dependent power law of sufficiently small exponent, display superdiffusion, L´evy flights and robustness properties very different from the scale-free networks. It has been proposed that these networks, found both in society and in biology, be classified as a new structure, the fractional networks. Particular important examples are the social networks and the modular hierarchical brain networks where both short- and long-range connections are present. The anomalous superdiffusive and the mixed diffusion behavior of these networks is studied here as well as its relation to the nature and density of the long-range connections.info:eu-repo/semantics/publishedVersio

The failure tolerance of mechatronic software systems to random and targeted attacks

This paper describes a complex networks approach to study the failure tolerance of mechatronic software systems under various types of hardware and/or software failures. We produce synthetic system architectures based on evidence of modular and hierarchical modular product architectures and known motifs for the interconnection of physical components to software. The system architectures are then subject to various forms of attack. The attacks simulate failure of critical hardware or software. Four types of attack are investigated: degree centrality, betweenness centrality, closeness centrality and random attack. Failure tolerance of the system is measured by a 'robustness coefficient', a topological 'size' metric of the connectedness of the attacked network. We find that the betweenness centrality attack results in the most significant reduction in the robustness coefficient, confirming betweenness centrality, rather than the number of connections (i.e. degree), as the most conservative metric of component importance. A counter-intuitive finding is that "designed" system architectures, including a bus, ring, and star architecture, are not significantly more failure-tolerant than interconnections with no prescribed architecture, that is, a random architecture. Our research provides a data-driven approach to engineer the architecture of mechatronic software systems for failure tolerance.Comment: Proceedings of the 2013 ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA (In Print