Maksim Kitsak

Identification of influential spreaders in complex networks

Spreading of information, ideas or diseases can be conveniently modelled in the context of complex networks. An analysis now reveals that the most efficient spreaders are not always necessarily the most connected agents in a network. Instead, the position of an agent relative to the hierarchical topological organization of the network might be as important as its connectivity.

Hyperbolic geometry of complex networks

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.

Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks

We study the betweenness centrality of fractal and nonfractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to nonfractal models. We also show that nodes of both fractal and nonfractal scale-free networks have power-law betweenness centrality distribution P(C) approximately C(-delta). We find that for nonfractal scale-free networks delta=2, and for fractal scale-free networks delta=2-1/dB, where dB is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at the autonomous system level (N=20566), where N is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to nonfractal networks upon adding random edges to a fractal network. We show that the crossover length l*, separating fractal and nonfractal regimes, scales with dimension dB of the network as p(-1/dB), where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p.

Tissue Specificity of Human Disease Module

Genes carrying mutations associated with genetic diseases are present in all human cells; yet, clinical manifestations of genetic diseases are usually highly tissue-specific. Although some disease genes are expressed only in selected tissues, the expression patterns of disease genes alone cannot explain the observed tissue specificity of human diseases. Here we hypothesize that for a disease to manifest itself in a particular tissue, a whole functional subnetwork of genes (disease module) needs to be expressed in that tissue. Driven by this hypothesis, we conducted a systematic study of the expression patterns of disease genes within the human interactome. We find that genes expressed in a specific tissue tend to be localized in the same neighborhood of the interactome. By contrast, genes expressed in different tissues are segregated in distinct network neighborhoods. Most important, we show that it is the integrity and the completeness of the expression of the disease module that determines disease manifestation in selected tissues. This approach allows us to construct a disease-tissue network that confirms known and predicts unexpected disease-tissue associations.

Fractal boundaries of complex networks

We introduce the concept of the boundary of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundary nodes seen from a given node of complex networks. We find that for both Erdős-Renyi and scale-free model networks, as well as for several real networks, the boundaries have fractal properties. In particular, the number of boundaries nodes B follows a power law probability density function which scales as B-2. The clusters formed by the boundary nodes seen from a given node are fractals with a fractal dimension df≈2. We present analytical and numerical evidences supporting these results for a broad class of networks.

Hidden variables in bipartite networks.

We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables that control the appearance of links between node pairs. We derive analytic expressions for the degree distribution, degree correlations, the distribution of the number of common neighbors, and the bipartite clustering coefficient in these networks. We also establish the relationship between degrees of nodes in original bipartite networks and in their unipartite projections. We further demonstrate how hidden variable formalism can be applied to analyze topological properties of networks in certain bipartite network models, and verify our analytical results in numerical simulations.

Resilience and efficiency in transportation networks

Comparing traffic delays finds that some cities with efficient road networks are less resilient than inefficient cities. Urban transportation systems are vulnerable to congestion, accidents, weather, special events, and other costly delays. Whereas typical policy responses prioritize reduction of delays under normal conditions to improve the efficiency of urban road systems, analytic support for investments that improve resilience (defined as system recovery from additional disruptions) is still scarce. In this effort, we represent paved roads as a transportation network by mapping intersections to nodes and road segments between the intersections to links. We built road networks for 40 of the urban areas defined by the U.S. Census Bureau. We developed and calibrated a model to evaluate traffic delays using link loads. The loads may be regarded as traffic-based centrality measures, estimating the number of individuals using corresponding road segments. Efficiency was estimated as the average annual delay per peak-period auto commuter, and modeled results were found to be close to observed data, with the notable exception of New York City. Resilience was estimated as the change in efficiency resulting from roadway disruptions and was found to vary between cities, with increased delays due to a 5% random loss of road linkages ranging from 9.5% in Los Angeles to 56.0% in San Francisco. The results demonstrate that many urban road systems that operate inefficiently under normal conditions are nevertheless resilient to disruption, whereas some more efficient cities are more fragile. The implication is that resilience, not just efficiency, should be considered explicitly in roadway project selection and justify investment opportunities related to disaster and other disruptions.

Latent geometry of bipartite networks

Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

Integration of Molecular Interactome and Targeted Interaction Analysis to Identify a COPD Disease Network Module

The polygenic nature of complex diseases offers potential opportunities to utilize network-based approaches that leverage the comprehensive set of protein-protein interactions (the human interactome) to identify new genes of interest and relevant biological pathways. However, the incompleteness of the current human interactome prevents it from reaching its full potential to extract network-based knowledge from gene discovery efforts, such as genome-wide association studies, for complex diseases like chronic obstructive pulmonary disease (COPD). Here, we provide a framework that integrates the existing human interactome information with experimental protein-protein interaction data for FAM13A, one of the most highly associated genetic loci to COPD, to find a more comprehensive disease network module. We identified an initial disease network neighborhood by applying a random-walk method. Next, we developed a network-based closeness approach (CAB) that revealed 9 out of 96 FAM13A interacting partners identified by affinity purification assays were significantly close to the initial network neighborhood. Moreover, compared to a similar method (local radiality), the CAB approach predicts low-degree genes as potential candidates. The candidates identified by the network-based closeness approach were combined with the initial network neighborhood to build a comprehensive disease network module (163 genes) that was enriched with genes differentially expressed between controls and COPD subjects in alveolar macrophages, lung tissue, sputum, blood, and bronchial brushing datasets. Overall, we demonstrate an approach to find disease-related network components using new laboratory data to overcome incompleteness of the current interactome.

Towards a Generic Resilience Management, Quantification and Development Process: General Definitions, Requirements, Methods, Techniques and Measures, and Case Studies

Generic standards on risk management and functional safety (e.g. ISO 31000 and IEC 61508) and similar frameworks proved to be surprisingly efficient to trigger and consolidate a widely accepted and ever more effective best practice frontier for risk control. In particular, this includes fundamental and applied research activities to improve processes and to provide more advanced, interlinked and effective methods for risk control. However, this also included the identification of yet unresolved challenges and lacks of completeness. The present work goes beyond these frameworks to address the need for a joint approach to frame resilience management and quantification for system development and improvement. It is understood as extending classical risk control to creeping or sudden disruptive, unexpected (unexampled) events, as strongly focusing on technical systems and organizational capabilities to bounce back (better) and as providing generic (technical) resilience capabilities for such resilience response performance. To this end, the article presents general resilience requirements, a resilience management process, which systematically refers to a resilience method taxonomy, resilience levels as well as an applicability table of methods to different resilience management steps for each resilience level. Three case studies elucidate the approach: (i) disruption effect simulation for the Swiss energy grid, (ii) data-driven resilience of the urban transport system of Florence, and (iii) Ontario provincial resilience model in Canada. The approach comprises representative existing resilience concepts, definitions, quantifications as well as resilience generation and development processes. It supports the development of further refined resilience management and quantification processes and related improved methods in particular to cover jointly safety and security needs as well as their practical application to a wide range of socio-technical cyber-physical hybrid systems. This will foster credible certification of the resilience of critical infrastructure, of safety and security critical systems and devices.