More Like this

1. Neighborhood-based bridge node centrality tuple for complex network analysis

   https://doi.org/10.1007/s41109-021-00388-1  

   Meghanathan, Natarajan ( December 2021 , Applied Network Science)

   Abstract We define a bridge node to be a node whose neighbor nodes are sparsely connected to each other and are likely to be part of different components if the node is removed from the network. We propose a computationally light neighborhood-based bridge node centrality (NBNC) tuple that could be used to identify the bridge nodes of a network as well as rank the nodes in a network on the basis of their topological position to function as bridge nodes. The NBNC tuple for a node is asynchronously computed on the basis of the neighborhood graph of the node that comprises of the neighbors of the node as vertices and the links connecting the neighbors as edges. The NBNC tuple for a node has three entries: the number of components in the neighborhood graph of the node, the algebraic connectivity ratio of the neighborhood graph of the node and the number of neighbors of the node. We analyze a suite of 60 complex real-world networks and evaluate the computational lightness, effectiveness, efficiency/accuracy and uniqueness of the NBNC tuple vis-a-vis the existing bridgeness related centrality metrics and the Louvain community detection algorithm. 

   more » « less
2. Topological clustering of multilayer networks

   https://doi.org/10.1073/pnas.2019994118  

   Yuvaraj, Monisha ; Dey, Asim K. ; Lyubchich, Vyacheslav ; Gel, Yulia R. ; Poor, H. Vincent ( May 2021 , Proceedings of the National Academy of Sciences)

   Multilayer networks continue to gain significant attention in many areas of study, particularly due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socioenvironmental ecosystems. However, clustering of multilayer networks, especially using the information on higher-order interactions of the system entities, still remains in its infancy. In turn, higher-order connectivity is often the key in such multilayer network applications as developing optimal partitioning of critical infrastructures in order to isolate unhealthy system components under cyber-physical threats and simultaneous identification of multiple brain regions affected by trauma or mental illness. In this paper, we introduce the concepts of topological data analysis to studies of complex multilayer networks and propose a topological approach for network clustering. The key rationale is to group nodes based not on pairwise connectivity patterns or relationships between observations recorded at two individual nodes but based on how similar in shape their local neighborhoods are at various resolution scales. Since shapes of local node neighborhoods are quantified using a topological summary in terms of persistence diagrams, we refer to the approach as clustering using persistence diagrams (CPD). CPD systematically accounts for the important heterogeneous higher-order properties of node interactions within and in-between network layers and integrates information from the node neighbors. We illustrate the utility of CPD by applying it to an emerging problem of societal importance: vulnerability zoning of residential properties to weather- and climate-induced risks in the context of house insurance claim dynamics.

    

   more » « less
3. Robustness of interdependent geometric networks under inhomogeneous failures

   https://doi.org/10.23919/WIOPT.2018.8362877  

   Kamran, Khashayar ; Zhang, Jianan ; Yeh, Edmund ; Modiano, Eytan ( May 2018 , 2018 16th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt))

   Complex systems such as smart cities and smart power grids rely heavily on their interdependent components. The failure of a component in one network may lead to the failure of the supported component in another network. Components which support a large number of interdependent components may be more vulnerable to attacks and failures. In this paper, we study the robustness of two interdependent networks under node failures. By modeling each network using a random geometric graph (RGG), we study conditions for the percolation of two interdependent RGGs after in-homogeneous node failures. We derive analytical bounds on the interdependent degree thresholds (k 1 ,k 2 ), such that the interdependent RGGs percolate after removing nodes in G i that support more than k j nodes in G j (∀i, j ∈ {1, 2}, i ≠ j). We verify the bounds using numerical simulation, and show that there is a tradeoff between k 1 and k 2 for maintaining percolation after the failures. 

   more » « less
4. Connectivity, reproduction number, and mobility interact to determine communities’ epidemiological superspreader potential in a metapopulation network

   https://doi.org/10.1371/journal.pcbi.1008674  

   Lieberthal, Brandon ; Gardner, Allison M. ( March 2021 , PLOS Computational Biology)

   Althouse, Benjamin Muir (Ed.)

   Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number ( R ). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R . We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R , centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R , alter host movements, or both. 

   more » « less
5. Subcubic Equivalences between Graph Centrality Problems, APSP, and Diameter

   https://doi.org/10.1145/3563393  

   Abboud, Amir ; Grandoni, Fabrizio ; Vassilevska_Williams, Virginia ( January 2023 , ACM Transactions on Algorithms)

   Measuring the importance of a node in a network is a major goal in the analysis of social networks, biological systems, transportation networks, and so forth. Differentcentralitymeasures have been proposed to capture the notion of node importance. For example, thecenterof a graph is a node that minimizes the maximum distance to any other node (the latter distance is theradiusof the graph). Themedianof a graph is a node that minimizes the sum of the distances to all other nodes. Informally, thebetweenness centralityof a nodewmeasures the fraction of shortest paths that havewas an intermediate node. Finally, thereach centralityof a nodewis the smallest distancersuch that anys-tshortest path passing throughwhas eithersortin the ball of radiusraroundw.

   The fastest known algorithms to compute the center and the median of a graph and to compute the betweenness or reach centrality even of a single node take roughly cubic time in the numbernof nodes in the input graph. It is open whether these problems admit truly subcubic algorithms, i.e., algorithms with running time Õ(n^3-δ) for some constant δ > 0.¹

   We relate the complexity of the mentioned centrality problems to two classical problems for which no truly subcubic algorithm is known, namely All Pairs Shortest Paths (APSP) and Diameter. We show that Radius, Median, and Betweenness Centrality areequivalent under subcubic reductionsto APSP, i.e., that a truly subcubic algorithm for any of these problems implies a truly subcubic algorithm for all of them. We then show that Reach Centrality is equivalent to Diameter under subcubic reductions. The same holds for the problem of approximating Betweenness Centrality within any finite factor. Thus, the latter two centrality problems could potentially be solved in truly subcubic time, even if APSP required essentially cubic time.

   On the positive side, our reductions for Reach Centrality imply an improved Õ(Mn^ω)-time algorithm for this problem in case of non-negative integer weights upper bounded byM, where ω is a fast matrix multiplication exponent.

    

   more » « less