Controllability and observability analysis for vertex domination centrality in directed networks.
ABSTRACT: Topological centrality is a significant measure for characterising the relative importance of a node in a complex network. For directed networks that model dynamic processes, however, it is of more practical importance to quantify a vertex's ability to dominate (control or observe) the state of other vertices. In this paper, based on the determination of controllable and observable subspaces under the global minimum-cost condition, we introduce a novel direction-specific index, domination centrality, to assess the intervention capabilities of vertices in a directed network. Statistical studies demonstrate that the domination centrality is, to a great extent, encoded by the underlying network's degree distribution and that most network positions through which one can intervene in a system are vertices with high domination centrality rather than network hubs. To analyse the interaction and functional dependence between vertices when they are used to dominate a network, we define the domination similarity and detect significant functional modules in glossary and metabolic networks through clustering analysis. The experimental results provide strong evidence that our indices are effective and practical in accurately depicting the structure of directed networks.
Project description:Power is a central phenomenon in societies. So for ages, numerous power perceptions in philosophy and sociology have existed. Measuring power of an actor in its social fabric is a difficult issue, however. After sketching first attempts for this in social network analyses, we develop a new power theory. To this end, we distinguish between vertices in the network and actors acting in vertices. Vertices get structural power potential from their position in the net. In an entropy-driven model such potential can be calculated for all vertices; for selected networks, the method is exemplified. Actors in vertices can deploy power potential once they have respective personal skills, and dominate actors in adjacent vertices. If chosen with suitable care, an alliance of actors can even dominate the whole network. The findings are applied to the famous 9/11-network with 34 vertices and 93 edges.
Project description:In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexes
Project description:Complex network theory (CNT) is gaining a lot of attention in the scientific community, due to its capability to model and interpret an impressive number of natural and anthropic phenomena. One of the most active CNT field concerns the evaluation of the centrality of vertices and edges in the network. Several metrics have been proposed, but all of them share a topological point of view, namely centrality descends from the local or global connectivity structure of the network. However, vertices can exhibit their own intrinsic relevance independent from topology; e.g., vertices representing strategic locations (e.g., hospitals, water and energy sources, etc.) or institutional roles (e.g., presidents, agencies, etc.). In these cases, the connectivity network structure and vertex intrinsic relevance mutually concur to define the centrality of vertices and edges. The purpose of this work is to embed the information about the intrinsic relevance of vertices into CNT tools to enhance the network analysis. We focus on the degree, closeness and betweenness metrics, being among the most used. Two examples, concerning a social (the historical Florence family's marriage network) and an infrastructure (a water supply system) network, demonstrate the effectiveness of the proposed relevance-embedding extension of the centrality metrics.
Project description:We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network's degree distribution. We show that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
Project description:<h4>Background</h4>Detection of central nodes in asymmetrically directed biological networks depends on centrality metrics quantifying individual nodes' importance in a network. In topological analyses on metabolic networks, various centrality metrics have been mostly applied to metabolite-centric graphs. However, centrality metrics including those not depending on high connections are largely unexplored for directed reaction-centric graphs.<h4>Results</h4>We applied directed versions of centrality metrics to directed reaction-centric graphs of microbial metabolic networks. To investigate the local role of a node, we developed a novel metric, cascade number, considering how many nodes are closed off from information flow when a particular node is removed. High modularity and scale-freeness were found in the directed reaction-centric graphs and betweenness centrality tended to belong to densely connected modules. Cascade number and bridging centrality identified cascade subnetworks controlling local information flow and irreplaceable bridging nodes between functional modules, respectively. Reactions highly ranked with bridging centrality and cascade number tended to be essential, compared to reactions that other central metrics detected.<h4>Conclusions</h4>We demonstrate that cascade number and bridging centrality are useful to identify key reactions controlling local information flow in directed reaction-centric graphs of microbial metabolic networks. Knowledge about the local flow connectivity and connections between local modules will contribute to understand how metabolic pathways are assembled.
Project description:In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from a practical point of view. In this contribution, we present a module-based method to efficiently fragment complex networks. The procedure firstly identifies topological communities through which the network can be represented using a well established heuristic algorithm of community finding. Then only the nodes that participate of inter-community links are removed in descending order of their betweenness centrality. We illustrate the method by applying it to a variety of examples in the social, infrastructure, and biological fields. It is shown that the module-based approach always outperforms targeted attacks to vertices based on node degree or betweenness centrality rankings, with gains in efficiency strongly related to the modularity of the network. Remarkably, in the US power grid case, by deleting 3% of the nodes, the proposed method breaks the original network in fragments which are twenty times smaller in size than the fragments left by betweenness-based attack.
Project description:Betweenness centrality is an indicator of a node's centrality in a network. It is equal to the number of shortest paths from all vertices to all others that pass through that node. Most of real-world large networks display a hierarchical community structure, and their betweenness computation possesses rather high complexity. Here we propose a new hierarchical decomposition approach to speed up the betweenness computation of complex networks. The advantage of this new method is its effective utilization of the local structural information from the hierarchical community. The presented method can significantly speed up the betweenness calculation. This improvement is much more evident in those networks with numerous homogeneous communities. Furthermore, the proposed method features a parallel structure, which is very suitable for parallel computation. Moreover, only a small amount of additional computation is required by our method, when small changes in the network structure are restricted to some local communities. The effectiveness of the proposed method is validated via the examples of two real-world power grids and one artificial network, which demonstrates that the performance of the proposed method is superior to that of the traditional method.
Project description:BACKGROUND:We examine the accuracy of enzyme catalytic residue predictions from a network representation of protein structure. In this model, amino acid alpha-carbons specify vertices within a graph and edges connect vertices that are proximal in structure. Closeness centrality, which has shown promise in previous investigations, is used to identify important positions within the network. Closeness centrality, a global measure of network centrality, is calculated as the reciprocal of the average distance between vertex i and all other vertices. RESULTS:We benchmark the approach against 283 structurally unique proteins within the Catalytic Site Atlas. Our results, which are inline with previous investigations of smaller datasets, indicate closeness centrality predictions are statistically significant. However, unlike previous approaches, we specifically focus on residues with the very best scores. Over the top five closeness centrality scores, we observe an average true to false positive rate ratio of 6.8 to 1. As demonstrated previously, adding a solvent accessibility filter significantly improves predictive power; the average ratio is increased to 15.3 to 1. We also demonstrate (for the first time) that filtering the predictions by residue identity improves the results even more than accessibility filtering. Here, we simply eliminate residues with physiochemical properties unlikely to be compatible with catalytic requirements from consideration. Residue identity filtering improves the average true to false positive rate ratio to 26.3 to 1. Combining the two filters together has little affect on the results. Calculated p-values for the three prediction schemes range from 2.7E-9 to less than 8.8E-134. Finally, the sensitivity of the predictions to structure choice and slight perturbations is examined. CONCLUSION:Our results resolutely confirm that closeness centrality is a viable prediction scheme whose predictions are statistically significant. Simple filtering schemes substantially improve the method's predicted power. Moreover, no clear effect on performance is observed when comparing ligated and unligated structures. Similarly, the CC prediction results are robust to slight structural perturbations from molecular dynamics simulation.
Project description:Vancomycin-resistant Enterococcus faecium (VRE) is a leading cause of hospital-acquired infections. This is particularly true in immunocompromised patients, where the damage to the microbiota caused by antibiotics can lead to VRE domination of the intestine, increasing a patient's risk for bloodstream infection. In previous studies we observed that the intestinal domination by VRE of patients hospitalized to receive allogeneic bone marrow transplantation can persist for weeks, but little is known about subspecies diversification and evolution during prolonged domination. Here we combined a longitudinal analysis of patient data and in vivo experiments to reveal previously unappreciated subspecies dynamics during VRE domination that appeared to be stable from 16S rRNA microbiota analyses. Whole-genome sequencing of isolates obtained from sequential stool samples provided by VRE-dominated patients revealed an unanticipated level of VRE population complexity that evolved over time. In experiments with ampicillin-treated mice colonized with a single CFU, VRE rapidly diversified and expanded into distinct lineages that competed for dominance. Mathematical modeling shows that in vivo evolution follows mostly a parabolic fitness landscape, where each new mutation provides diminishing returns and, in the setting of continuous ampicillin treatment, reveals a fitness advantage for mutations in penicillin-binding protein 5 (pbp5) that increase resistance to ampicillin. Our results reveal the rapid diversification of host-colonizing VRE populations, with implications for epidemiologic tracking of in-hospital VRE transmission and susceptibility to antibiotic treatment.
Project description:Meiotic mapping of quantitative trait loci regulating expression (eQTLs) has allowed the construction of gene networks. However, the limited mapping resolution of these studies has meant that genotype data are largely ignored, leading to undirected networks that fail to capture regulatory hierarchies. Here we use high resolution mapping of copy number eQTLs (ceQTLs) in a mouse-hamster radiation hybrid (RH) panel to construct directed genetic networks in the mammalian cell. The RH network covering 20,145 mouse genes had significant overlap with, and similar topological structures to, existing biological networks. Upregulated edges in the RH network had significantly more overlap than downregulated. This suggests repressive relationships between genes are missed by existing approaches, perhaps because the corresponding proteins are not present in the cell at the same time and therefore unlikely to interact. Gene essentiality was positively correlated with connectivity and betweenness centrality in the RH network, strengthening the centrality-lethality principle in mammals. Consistent with their regulatory role, transcription factors had significantly more outgoing edges (regulating) than incoming (regulated) in the RH network, a feature hidden by conventional undirected networks. Directed RH genetic networks thus showed concordance with pre-existing networks while also yielding information inaccessible to current undirected approaches.