1,720,986 research outputs found
Bond and site color-avoiding percolation in scale-free networks
No full textRecently, the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one vulnerability (color), a robust color-avoiding connectivity is possible. However, many infrastructure networks show the problem of vulnerable classes of edges instead of vertices. Here we formulate color-avoiding percolation for colored edges as well. Additionally, we allow for random failures of vertices or edges. The interplay of random failures and possible collective failures implies a rich phenomenology. An interesting form of critical behavior is found for networks with a power-law degree distribution independent of the number of colors, but still dependent on the existence of the colors and therefore different from standard percolation. Our percolation framework fills a gap between different multilayer network percolation scenarios
A PageRank-based preferential attachment model for the evolution of the World Wide Web
No full textWe propose a model of network growth aimed at mimicking the evolution of theWorld Wide Web. To this purpose, we take as a key quantity, in the network evolution, the centrality or importance of a vertex as measured by its PageRank. Using a preferential attachment rule and a rewiring procedure based on this quantity, we can reproduce most of the topological properties of the system. Copyright © EPLA, 2010
Robustness and assortativity for diffusion-like processes in scale-free networks
No full textBy analysing the diffusive dynamics of epidemics and of distress in complex networks, we study the effect of the assortativity on the robustness of the networks. We first determine by spectral analysis the thresholds above which epidemics/failures can spread; we then calculate the slowest diffusional times. Our results shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize, while in assortative networks there is a longer time for intervention before epidemic/failure spreads. Moreover, we study by computer simulations the sandpile cascade model, a diffusive model of distress propagation (financial contagion). We show that, while assortative networks are more prone to the propagation of epidemic/failures, degree-targeted immunization policies increases their resilience to systemic risk. © 2012 Europhysics Letters Association
Mitigating cascades in sandpile models: an immunization strategy for systemic risk?
No full textWe use a simple model of distress propagation (the sandpile model) to show how financial systems are naturally subject to the risk of systemic failures. Taking into account possible network structures among financial institutions, we investigate if simple policies can limit financial distress propagation to avoid system-wide crises, i.e. to dampen systemic risk. We therefore compare different immunization policies (i.e. targeted helps to financial institutions) and find that the information coming from the network topology allows to mitigate systemic cascades by targeting just few institutions
Population dynamics on complex food webs
No full textIn this work we analyze the topological and dynamical properties of a simple model of complex food webs, namely the niche model. In order to underline competition among species, we introduce "prey" and "predators" weighted overlap graphs derived from the niche model and compare synthetic food webs with real data. Doing so, we find new tests for the goodness of synthetic food web models and indicate a possible direction of improvement for existing ones. We then exploit the weighted overlap graphs to define a competition kernel for LotkaVolterra population dynamics and find that for such a model the stability of food webs decreases with its ecological complexity. © 2011 World Scientific Publishing Company
Bi-stability of SUDR+K model of epidemics and test kits applied to COVID-19
No full textMotivated by the many diverse responses of different countries to the COVID-19 emergency, here we develop a toy model of the dependence of the epidemics spreading on the availability of tests for disease. Our model, that we call SUDR+K, grounds on the usual SIR model, with the difference of splitting the total fraction of infected individuals in two components: patients that are still undetected and patients that have been already detected through tests. Moreover, we assume that available tests increase at a constant rate from the beginning of epidemics but are consumed to detect infected individuals. Strikingly, we find a bi-stable behavior between a phase with a giant fraction of infected and a phase with a very small fraction. We show that the separation between these two regimes is governed by a match between the rate of testing and a rate of infection spread at given time. We also show that the existence of two phases does not depend on the mathematical choice of the form of the term describing the rate at which undetected individuals are tested and detected. Presented research implies that a vigorous early testing activity, before the epidemics enters its giant phase, can potentially keep epidemics under control, and that even a very small change of the testing rate around the bi-stable point can determine a fluctuation of the size of the whole epidemics of various orders of magnitude. For the real application of realistic model to ongoing epidemics, we would gladly collaborate with field epidemiologists in order to develop quantitative models of testing process
Hypergraph topological quantities for tagged social networks
Full text linkRecent years have witnessed the emergence of a new class of social networks, which require us to move beyond previously employed representations of complex graph structures. A notable example is that of the folksonomy, an online process where users collaboratively employ tags to resources to impart structure to an otherwise undifferentiated database. In a recent paper, we proposed a mathematical model that represents these structures as tripartite hypergraphs and defined basic topological quantities of interest. In this paper, we extend our model by defining additional quantities such as edge distributions, vertex similarity and correlations as well as clustering. We then empirically measure these quantities on two real life folksonomies, the popular online photo sharing site Flickr and the bookmarking site CiteULike. We find that these systems share similar qualitative features with the majority of complex networks that have been previously studied. We propose that the quantities and methodology described here can be used as a standard tool in measuring the structure of tagged networks
Networks with arbitrary edge multiplicities
Full text linkOne of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of triangles in which edges, rather than vertices, participate. Here we show that the multiplicity distribution of real networks is in many cases scale free, and in general very broad. Thus, besides the fact that in real networks the number of edges attached to vertices often has a scale-free distribution, we find that the number of triangles attached to edges can have a scale-free distribution as well. We show that current models, even when they generate clustered networks, systematically fail to reproduce the observed multiplicity distributions. We therefore propose a generalized model that can reproduce networks with arbitrary distributions of vertex degrees and edge multiplicities, and study many of its properties analytically
Topologically biased random walk and community finding in networks
Full text linkWe present an approach of topology biased random walks for undirected networks. We focus on a one-parameter family of biases, and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion to study the features of random walks vs parameter values. Furthermore, we show an analysis of the spectral gap maximum associated with the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow ad hoc algorithms for the exploration of complex networks and their communities
Random hypergraphs and their applications
Full text linkIn the last few years we have witnessed the emergence, primarily in online communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folksonomy, a tripartite structure of users, resources, and tags—labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures that represents them as random hypergraphs. We show that it is possible to calculate many properties of this model exactly in the limit of large network size and we compare the results against observations of a real folksonomy, that of the online photography website Flickr. We show that in some cases the model matches the properties of the observed network well, while in others there are significant differences, which we find to be attributable to the practice of multiple tagging, i.e., the application by a single user of many tags to one resource or one tag to many resource
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