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      Modularity produces small-world networks with dynamical time-scale separation

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          Abstract

          The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as small-world networks (SWN). We show that modular organization in otherwise random networks generically give rise to SWN, with a characteristic time-scale separation between fast intra-modular and slow inter-modular processes. The universality of this dynamical signature, that distinguishes modular networks from earlier models of SWN, is demonstrated by processes as different as spin-ordering, synchronization and diffusion.

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          Functional cartography of complex metabolic networks

          , (2005)
          High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks. Specifically, we demonstrate that one can (i) find functional modules in complex networks, and (ii) classify nodes into universal roles according to their pattern of intra- and inter-module connections. The method thus yields a ``cartographic representation'' of complex networks. Metabolic networks are among the most challenging biological networks and, arguably, the ones with more potential for immediate applicability. We use our method to analyze the metabolic networks of twelve organisms from three different super-kingdoms. We find that, typically, 80% of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we find that low-degree metabolites that connect different modules are more conserved than hubs whose links are mostly within a single module.
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            Compartments revealed in food-web structure.

            Compartments in food webs are subgroups of taxa in which many strong interactions occur within the subgroups and few weak interactions occur between the subgroups. Theoretically, compartments increase the stability in networks, such as food webs. Compartments have been difficult to detect in empirical food webs because of incompatible approaches or insufficient methodological rigour. Here we show that a method for detecting compartments from the social networking science identified significant compartments in three of five complex, empirical food webs. Detection of compartments was influenced by food web resolution, such as interactions with weights. Because the method identifies compartmental boundaries in which interactions are concentrated, it is compatible with the definition of compartments. The method is rigorous because it maximizes an explicit function, identifies the number of non-overlapping compartments, assigns membership to compartments, and tests the statistical significance of the results. A graphical presentation reveals systemic relationships and taxa-specific positions as structured by compartments. From this graphic, we explore two scenarios of disturbance to develop a hypothesis for testing how compartmentalized interactions increase stability in food webs.
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              Subnetwork hierarchies of biochemical pathways.

              The vastness and complexity of the biochemical networks that have been mapped out by modern genomics calls for decomposition into subnetworks. Such networks can have inherent non-local features that require the global structure to be taken into account in the decomposition procedure. Furthermore, basic questions such as to what extent the network (graph theoretically) can be said to be built by distinct subnetworks are little studied. We present a method to decompose biochemical networks into subnetworks based on the global geometry of the network. This method enables us to analyze the full hierarchical organization of biochemical networks and is applied to 43 organisms from the WIT database. Two types of biochemical networks are considered: metabolic networks and whole-cellular networks (also including for example information processes). Conceptual and quantitative ways of describing the hierarchical ordering are discussed. The general picture of the metabolic networks arising from our study is that of a few core-clusters centred around the most highly connected substances enclosed by other substances in outer shells, and a few other well-defined subnetworks. An implementation of our algorithm and other programs for analyzing the data is available from http://www.tp.umu.se/forskning/networks/meta/ Supplementary material is available at http://www.tp.umu.se/forskning/networks/meta/
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                Author and article information

                Journal
                25 February 2008
                2009-04-07
                Article
                10.1209/0295-5075/85/68006
                0802.3671
                e3a748db-72fa-4be0-9fdf-12e0c7770220

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Europhys. Lett. 85, 68006 (2009)
                6 pages, 7 figures. Published version, Results and figures of additional dynamics have been included
                physics.bio-ph cond-mat.dis-nn physics.soc-ph

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