Configuring Random Graph Models with Fixed Degree Sequences

Fosdick, Bailey K.; Larremore, Daniel B.; Nishimura, Joel; Ugander, Johan

doi:10.48550/arxiv.1608.00607

Cited by 11 publications

(32 citation statements)

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“…ples the configuration model-multi-edges and self-loops are allowed-and leaves the degree sequence unaltered [8]. The rewiring rate ω ≥ 0 permits us to easily tune the interplay between the disease propagation and the structural dynamics.…”

Section: Regimementioning

confidence: 99%

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks

et al. 2018

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We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework on a given degree distribution, we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the SIS process. This analysis is suitable for the characterization of the phase transition and leads to three main contributions. (i) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (ii) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (iii) We obtain bounds for the critical exponents of a number of quantities in the stationary state. This allows us to reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon : observables for different degree classes have a different scaling with the infection rate. This phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold.

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Section: Regimementioning

confidence: 99%

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks

et al. 2018

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“…There are reflective boundary conditions at x = 0 and x = 1 and periodic boundary conditions at y = 0 and y = 1. We create edges between nearby nodes according to equation (27). Edges are deleted at the rate given by equation (28).…”

Section: B Example Scenario: Local State Degree Distributionmentioning

confidence: 99%

“…We first consider networks in which there is no edge deletion (i.e., D ≡ 0). We take the edge-creation rate to be 500/n times that given in equation (27). We choose all other parameters as in Section VI B.…”

Section: Limit Of Large Networkmentioning

confidence: 99%

“…We now introduce edge deletion and choose D to be given by equation (28). We increase the rate of edge creation slightly by taking the edge-creation rate to be 750/n times that given in equation (27). We show the resulting mean degree distribution sampled over 10 6 /n realizations of Algorithm 1 for n = 125, n = 500, n = 2000, and n = 8000 in the bottom panel of Fig.…”

Section: Limit Of Large Networkmentioning

confidence: 99%

“…(Top) No edge deletion (i.e., D ≡ 0), and the edge-creation rate is 500/n times that given in equation ( 27). (Bottom) The edge deletion is given by equation (28), and the edge creation rate 750/n times that given in equation (27). The other parameter values are as in Section VI B.…”

Section: One-step Network Creation Versus Kinetic Approximationsmentioning

confidence: 99%

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Mean-field approach to evolving spatial networks, with an application to osteocyte network formation

et al. 2017

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We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or it can have some more abstract internal property that describes something like a social trait. Edges between nodes are created and destroyed, and new nodes enter the system. We introduce a "local state degree distribution" (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes, but with a smaller number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis.

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Network science approach to modelling the topology and robustness of supply chain networks: a review and perspective

2017

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Due to the increasingly complex and interconnected nature of global supply chain networks (SCNs), a recent strand of research has applied network science methods to model SCN growth and subsequently analyse various topological features, such as robustness. This paper provides: (1) a comprehensive review of the methodologies adopted in literature for modelling the topology and robustness of SCNs; (2) a summary of topological features of the real world SCNs, as reported in various data driven studies; and (3) a discussion on the limitations of existing network growth models to realistically represent the observed topological characteristics of SCNs. Finally, a novel perspective is proposed to mimic the SCN topologies reported in empirical studies, through fitness based generative network models.

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Configuring Random Graph Models with Fixed Degree Sequences

Cited by 11 publications

References 0 publications

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks

Mean-field approach to evolving spatial networks, with an application to osteocyte network formation

Network science approach to modelling the topology and robustness of supply chain networks: a review and perspective

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