A population evolution model and its applications to random networks

Fazekas, István; Noszály, Cs.; Perecsényi, Attila

doi:10.48550/arxiv.1604.01579

Cited by 2 publications

(3 citation statements)

References 8 publications

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“…[18]). As the calculation above shows, this model fits into the general framework of [19] or [22] for single-type preferential attachment random graphs. 5.2.…”

mentioning

confidence: 74%

“…Generalized Barabási-Albert random graph. This is a multi-type version and a generalization (or modification) of the graph model in [4], specified in [8] (see also [18,19,22] for general setups). The dynamics of this model is the following: for every n ≥ 1, in the nth step, the new vertex v n attaches with M n (not necessarily different) edges to some of the old vertices, where M n is a positive integer valued random variable, which is independent of F n−1 .…”

Section: Theorem 1 If a Random Sequence Of Graphs With Multi-type Edg...mentioning

confidence: 99%

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

Backhausz¹,

Rozner²

2017

Preprint

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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 = (d1, d2, . . . , dN ), where d k ∈ Z + 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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“…[18]). As the calculation above shows, this model fits into the general framework of [19] or [22] for single-type preferential attachment random graphs. 5.2.…”

mentioning

confidence: 74%

Section: Theorem 1 If a Random Sequence Of Graphs With Multi-type Edg...mentioning

confidence: 99%

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

Backhausz¹,

Rozner²

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…In [23] power law degree distribution was proved for the PA-class. In [18] the PA-class was extended to describe the evolution of certain populations. In [2], [3] and [16] the above mentioned ideas of Cooper and Frieze [12] were applied, but instead of the original preferential attachment rule, the vertices were chosen according to the weights of certain cliques.…”

Section: Introductionmentioning

confidence: 99%

The $N$-stars network evolution model

Fazekas,

Noszály,

Perecsényi

2019

Preprint

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A new network evolution model is introduced in this paper. The model is based on co-operations of N units. The units are the nodes of the network and the cooperations are indicated by directed links. At each evolution step N units co-operate which formally means that they form a directed N -star subgraph. At each step either a new unit joins to the network and it co-operates with N − 1 old units or N old units co-operate. During the evolution both preferential attachment and uniform choice are applied. Asymptotic power law distributions are obtained both for the in-degrees and the out-degrees.

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A population evolution model and its applications to random networks

Cited by 2 publications

References 8 publications

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

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

The $N$-stars network evolution model

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