58,678 research outputs found

    On fast-slow consensus networks with a dynamic weight

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    We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take values over the whole real numbers, and that its behaviour depends on the nodes it connects and on an extrinsic slow variable. We show that, under mild conditions on the weight, there exists a reduction such that the dynamics of the network are organized by a transcritical singularity. As such, we detail a slow passage through a transcritical singularity for a simple network, and we observe that an exchange between consensus and clustering of the nodes is possible. In contrast to the classical planar fast-slow transcritical singularity, the network structure of the system under consideration induces the presence of a maximal canard. Our main tool of analysis is the blow-up method. Thus, we also focus on tracking the effects of the blow-up transformation on the network's structure. We show that on each blow-up chart one recovers a particular dynamic network related to the original one. We further indicate a numerical issue produced by the slow passage through the transcritical singularity

    The Naming Game in Social Networks: Community Formation and Consensus Engineering

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    We study the dynamics of the Naming Game [Baronchelli et al., (2006) J. Stat. Mech.: Theory Exp. P06014] in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. We find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.Comment: The original publication is available at http://www.springerlink.com/content/70370l311m1u0ng3

    Hearing the clusters in a graph: A distributed algorithm

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    We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies

    Consensus clustering in complex networks

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    The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on the specific random seeds, initial conditions and tie-break rules adopted for their execution. Consensus clustering is used in data analysis to generate stable results out of a set of partitions delivered by stochastic methods. Here we show that consensus clustering can be combined with any existing method in a self-consistent way, enhancing considerably both the stability and the accuracy of the resulting partitions. This framework is also particularly suitable to monitor the evolution of community structure in temporal networks. An application of consensus clustering to a large citation network of physics papers demonstrates its capability to keep track of the birth, death and diversification of topics.Comment: 11 pages, 12 figures. Published in Scientific Report

    Dynamical and topological aspects of consensus formation in complex networks

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    The present work analyzes a particular scenario of consensus formation, where the individuals navigate across an underlying network defining the topology of the walks. The consensus, associated to a given opinion coded as a simple message, is generated by interactions during the agent's walk and manifest itself in the collapse of the various opinions into a single one. We analyze how the topology of the underlying networks and the rules of interaction between the agents promote or inhibit the emergence of this consensus. We find that non-linear interaction rules are required to form consensus and that consensus is more easily achieved in networks whose degree distribution is narrower.Fil: Chacoma, Andrés Alberto. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Mato, German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Kuperman, Marcelo Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentin

    Primerjava algoritmov za odkrivanje skupnosti v omrežjih na osnovi izmenjave oznak

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    Community structure is an important property of complex networks, since it reveals the organization of the network and relationships between its members. Therefore, the analysis of community structure and development of effective procedures for its detection has been one of the main focuses of network theory. Numerous methods have been proposed for detecting community structure in networks cite{article7}. This thesis presents a heuristic community detection algorithm based on label propagation. Due to its simplicity and low time complexity, label propagation algorithm should be the first option to provide a better understanding of the network community structure before examining other more complex alternatives. We give a brief introduction to graphs and networks, different clustering metrics and related work in the field of network community detection. Next, we present the basic approach of label propagation algorithm, discuss advantages and disadvantages, and review extensions of the method, focusing mainly on consensus clustering and fast consensus clustering. The aforementioned algorithms are implemented in a Python programming library, which is available at: url{https://github.com/damir1407/label-propagation}. Furthermore, we evaluate these three network clustering methods on different synthetic and real-world networks, and present the results. The thesis is concluded with a summary of the presented methods and directions for future work.Struktura skupnosti je pomembna lastnost kompleksnih omrežij, saj razkrije organizacijo omrežja in razmerja med njegovimi člani. Zato sta analiza skupnosti in razvoj učinkovitih načinov za njihovo odkrivanje dva izmed pomembnih žarišč teorije omrežij. V literaturi so predlagani številni načini za odkrivanje strukture skupnosti v omrežjih~cite{article7}. V tej diplomski nalogi je predstavljen hevrističen algoritem za odkrivanje skupnosti, ki temelji na izmenjavi oznak. Zaradi njegove enostavnosti in nizke časovne zahtevnosti, bi moral biti algoritem za izmenjavo oznak prva izbira pri zagotavljanju boljšega razumevanja strukture skupnosti v omrežjih, pred proučevanjem drugih, bolj zapletenih alternativ. Začnemo s kratkim uvodom v grafe in omrežja, različne metrike gručenja in raziskave, ki se nanašajo na področje odkrivanja skupnosti v omrežjih. Potem predstavimo osnovne pristope algoritma za izmenjavo oznak, razpravljamo o njegovih prednostih in pomanjkljivostih, ter pregledamo razširitve metode s poudarkom na konsenznem gručenju in hitrem konsenznem gručenju. Zgoraj omenjeni algoritmi so implementirani v programski knjižnici za Python, ki je na voljo na: url{https://github.com/damir1407/label-propagation}. V nadaljevanju ocenimo učinkovitost teh treh metod gručenja omrežij na različnih sintetičnih in resničnih omrežjih ter predstavimo rezultate. Diplomsko nalogo zaključimo s povzetkom predstavljenih metod in predlogi za prihodnje delo
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