Dynamics of influence on hierarchical structures

Fotouhi, Babak; Rabbat, Michael

doi:10.1103/physreve.88.022105

Cited by 8 publications

(10 citation statements)

References 66 publications

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“…where, as mentioned above, and repeated here for convenience of reference, we have c = 1 − ζ ζ+(2β+θ)t β 2β+θ , and also ζ = 2L(0) + θN (0) is obtained from initial conditions. Note that for the special case of θ = 0, the result in (10) correctly reduces to that previously found in the literature [54].…”

Section: Evolution Of the Degreessupporting

confidence: 85%

Temporal dynamics of connectivity and epidemic properties of growing networks

Fotouhi

Shirkoohi

2016

Phys. Rev. E

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Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by incorporating the temporal aspects of networks of contacts, societal and online, that are of interest in the study of epidemics (and other similar diffusion processes). However, temporal dynamics have predominantly focused on link fluctuations and nodal activities, and less attention has been paid to the growth of the underlying network. Many real networks grow: Online networks are evidently in constant growth, and societal networks can grow due to migration flux and reproduction. The effect of network growth on the epidemic properties of networks is hitherto unknown, mainly due to the predominant focus of the network growth literature on the so-called steady state. This paper takes a step towards alleviating this gap. We analytically study the degree dynamics of a given arbitrary network that is subject to growth. We use the theoretical findings to predict the epidemic properties of the network as a function of time. We observe that the introduction of new individuals into the network can enhance or diminish its resilience against endemic outbreaks and investigate how this regime shift depends upon the connectivity of newcomers and on how they establish connections to existing nodes. Throughout, theoretical findings are corroborated with Monte Carlo simulations over synthetic and real networks. The results shed light on the effects of network growth on the future epidemic properties of networks and offers insights for devising a priori immunization strategies.

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Section: Evolution Of the Degreessupporting

confidence: 85%

Temporal dynamics of connectivity and epidemic properties of growing networks

Fotouhi

Shirkoohi

2016

Phys. Rev. E

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“…The binomial coefficient equals unity, and the result become identical to Equation (18), which is also obtained for example in [29,37]. Now we focus on the special case of M = 2, and confirm that it agrees with (17).…”

Section: Generalization Of Model 2 To M Layerssupporting

confidence: 67%

Growing multiplex networks with arbitrary number of layers

Momeni

Fotouhi

2015

Phys. Rev. E

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This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the special case of homogeneous growth, and are limited to the state state (that is, the limit of infinite size). In the present paper, we obtain closed-form solutions for the joint degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state. Heterogeneous growth means that each incoming node establishes different numbers of links in different layers. We consider both uniform and preferential growth. We then extend the analysis of the uniform growth mechanism to arbitrary times. We obtain a closedform solution for the time-dependent joint degree distribution of a growing multiplex network with arbitrary initial conditions. Throughout, theoretical findings are corroborated with Monte Carlo simulations. The results shed light on the effects of the initial network on the transient dynamics of growing multiplex networks, and takes a step towards characterizing the temporal variations of the connectivity of growing multiplex networks, as well as predicting their future structural properties.

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“…A parallel finding is that the initial network structure also matters for the Barabási-Albert growing network model [35,36], offering the possibility that the initial conditions and onset of the preferential attachment mechanism may be estimated from an observed network. For even relatively small seed networks with average degree 10, the asymptotic behavior of the degree distribution will not match the classic k −3 form found in [9].…”

Section: Discussionmentioning

confidence: 94%

Simon's fundamental rich-get-richer model entails a dominant first-mover advantage

et al. 2017

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Herbert Simon's classic rich-get-richer model is one of the simplest empirically supported mechanisms capable of generating heavy-tail size distributions for complex systems. Simon argued analytically that a population of flavored elements growing by either adding a novel element or randomly replicating an existing one would afford a distribution of group sizes with a power-law tail. Here, we show that, in fact, Simon's model does not produce a simple power law size distribution as the initial element has a dominant first-mover advantage, and will be overrepresented by a factor proportional to the inverse of the innovation probability. The first group's size discrepancy cannot be explained away as a transient of the model, and may therefore be many orders of magnitude greater than expected. We demonstrate how Simon's analysis was correct but incomplete, and expand our alternate analysis to quantify the variability of long term rankings for all groups. We find that the expected time for a first replication is infinite, and show how an incipient group must break the mechanism to improve their odds of success. We present an example of citation counts for a specific field that demonstrates a first-mover advantage consistent with our revised view of the rich-getricher mechanism. Our findings call for a reexamination of preceding work invoking Simon's model and provide an expanded understanding going forward.

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Dynamics of influence on hierarchical structures

Cited by 8 publications

References 66 publications

Temporal dynamics of connectivity and epidemic properties of growing networks

Temporal dynamics of connectivity and epidemic properties of growing networks

Growing multiplex networks with arbitrary number of layers

Simon's fundamental rich-get-richer model entails a dominant first-mover advantage

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