18,912 research outputs found
Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks
We investigate a fermionic susceptible-infected-susceptible model with
mobility of infected individuals on uncorrelated scale-free networks with
power-law degree distributions of exponents
. Two diffusive processes with diffusion rate of an infected
vertex are considered. In the \textit{standard diffusion}, one of the
nearest-neighbors is chosen with equal chance while in the \textit{biased
diffusion} this choice happens with probability proportional to the neighbor's
degree. A non-monotonic dependence of the epidemic threshold on with an
optimum diffusion rate , for which the epidemic spreading is more
efficient, is found for standard diffusion while monotonic decays are observed
in the biased case. The epidemic thresholds go to zero as the network size is
increased and the form that this happens depends on the diffusion rule and
degree exponent. We analytically investigated the dynamics using quenched and
heterogeneous mean-field theories. The former presents, in general, a better
performance for standard and the latter for biased diffusion models, indicating
different activation mechanisms of the epidemic phases that are rationalized in
terms of hubs or max -core subgraphs.Comment: 9 pages, 4 figure
Clustering Algorithms for Scale-free Networks and Applications to Cloud Resource Management
In this paper we introduce algorithms for the construction of scale-free
networks and for clustering around the nerve centers, nodes with a high
connectivity in a scale-free networks. We argue that such overlay networks
could support self-organization in a complex system like a cloud computing
infrastructure and allow the implementation of optimal resource management
policies.Comment: 14 pages, 8 Figurs, Journa
Network Sampling: From Static to Streaming Graphs
Network sampling is integral to the analysis of social, information, and
biological networks. Since many real-world networks are massive in size,
continuously evolving, and/or distributed in nature, the network structure is
often sampled in order to facilitate study. For these reasons, a more thorough
and complete understanding of network sampling is critical to support the field
of network science. In this paper, we outline a framework for the general
problem of network sampling, by highlighting the different objectives,
population and units of interest, and classes of network sampling methods. In
addition, we propose a spectrum of computational models for network sampling
methods, ranging from the traditionally studied model based on the assumption
of a static domain to a more challenging model that is appropriate for
streaming domains. We design a family of sampling methods based on the concept
of graph induction that generalize across the full spectrum of computational
models (from static to streaming) while efficiently preserving many of the
topological properties of the input graphs. Furthermore, we demonstrate how
traditional static sampling algorithms can be modified for graph streams for
each of the three main classes of sampling methods: node, edge, and
topology-based sampling. Our experimental results indicate that our proposed
family of sampling methods more accurately preserves the underlying properties
of the graph for both static and streaming graphs. Finally, we study the impact
of network sampling algorithms on the parameter estimation and performance
evaluation of relational classification algorithms
Local majority dynamics on preferential attachment graphs
Suppose in a graph vertices can be either red or blue. Let be odd. At
each time step, each vertex in polls random neighbours and takes
the majority colour. If it doesn't have neighbours, it simply polls all of
them, or all less one if the degree of is even. We study this protocol on
the preferential attachment model of Albert and Barab\'asi, which gives rise to
a degree distribution that has roughly power-law ,
as well as generalisations which give exponents larger than . The setting is
as follows: Initially each vertex of is red independently with probability
, and is otherwise blue. We show that if is
sufficiently biased away from , then with high probability,
consensus is reached on the initial global majority within
steps. Here is the number of vertices and is the minimum of
and (or if is even), being the number of edges each new
vertex adds in the preferential attachment generative process. Additionally,
our analysis reduces the required bias of for graphs of a given degree
sequence studied by the first author (which includes, e.g., random regular
graphs)
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