Degree growth rates and index estimation in a directed preferential attachment model

Wang, Tiandong; Resnick, Sidney I.

doi:10.1016/j.spa.2019.03.021

Cited by 21 publications

(18 citation statements)

References 26 publications

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“…[2,8]), since theoretically the directed PA mechanism generates a network with the scale-free property because nodes with large degrees are likely to attract more edges than those with small degrees (cf. [14,15,18,20]). However, asymptotic behavior of the proportion of reciprocal edges in a directed PA model has not yet been explored in the literature.…”

Section: Introductionmentioning

confidence: 99%

Measuring Reciprocity in a Directed Preferential Attachment Network

Wang¹,

Resnick²

2021

Preprint

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Empirical studies [7,10] show that online social networks have not only inand out-degree distributions with Pareto-like tails, but also a high proportion of reciprocal edges. A classical directed preferential attachment (PA) model generates in-and out-degree distribution with power-law tails, but theoretical properties of the reciprocity feature in this model have not yet been studied. We derive the asymptotic results on the number of reciprocal edges between two fixed nodes, as well as the proportion of reciprocal edges in the entire PA network. We see that with certain choices of parameters, the proportion of reciprocal edges in a directed PA network is close to 0, which differs from the empirical observation. This points out one potential problem of fitting a classical PA model to a given network dataset with high reciprocity, and indicates alternative models need to be considered.

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Section: Introductionmentioning

confidence: 99%

Measuring Reciprocity in a Directed Preferential Attachment Network

Wang¹,

Resnick²

2021

Preprint

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“…Recently, and independently, Wang and Resnick [10] studied the special case of a DPA model where so that a node is always added. The focus of their paper is slightly different from that of the current paper.…”

Section: Introduction and Modelsmentioning

confidence: 99%

Directed preferential attachment models: Limiting degree distributions and their tails

Britton

2020

J. Appl. Probab.

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The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two independent pure birth processes that are observed at a common exponentially distributed time T (thus creating dependence between in- and out-degree). The characterization gives an explicit form for the joint degree distribution, and this confirms previously derived tail probabilities for the two marginal degree distributions. The new characterization is also used to obtain an explicit expression for tail probabilities in which both degrees are large. A new generalized directed preferential attachment model is then defined and analyzed using similar methods. The two extensions, motivated by empirical evidence, are to allow double-directed (i.e. undirected) edges in the network, and to allow the probability of connecting an ingoing (outgoing) edge to a specified node to also depend on the out-degree (in-degree) of that node.

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“…Different directed preferential attachment models were introduced in Refs. [7,25]. They examine a growing network in which a new vertex and a new edge is added to the graph in every step.…”

Section: Introductionmentioning

confidence: 99%

“…In Refs. [7,25], the asymptotic degree distribution is examined. In those models which are discussed in this article, we first choose the endpoint of the new vertex and then the type of the new edge is decided with probabilities depending on the structure of the graph.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic degree distribution in preferential attachment graph models with multiple type edges

Backhausz

Rozner

2019

Stochastic Models

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We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the N-type case, we define the (generalized) degree of a given vertex as d ¼ ðd 1 ; d 2 ;. .. ; d N Þ; where d k 2 Z þ 0 is the number of type k edges connected to it. We prove the existence of an a.s. asymptotic degree distribution for a general family of preferential attachment random graph models with multi-type edges. More precisely, we show that the proportion of vertices with (generalized) degree d tends to some random variable as the number of steps goes to infinity. We also provide recurrence equations for the asymptotic degree distribution. Finally, we generalize the scale-free property of random graphs to the multi-type case.

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Degree growth rates and index estimation in a directed preferential attachment model

Cited by 21 publications

References 26 publications

Measuring Reciprocity in a Directed Preferential Attachment Network

Measuring Reciprocity in a Directed Preferential Attachment Network

Directed preferential attachment models: Limiting degree distributions and their tails

Asymptotic degree distribution in preferential attachment graph models with multiple type edges

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