Degree sequences of geometric preferential attachment graphs

Jordan, Jonathan

doi:10.1017/s0001867800004079

Cited by 16 publications

(54 citation statements)

References 15 publications

(27 reference statements)

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“…With aims comparable to ours, several works discussed models obtained by modulating the rule of preferential attachment by a measure of proximity, see [17,2,23,22,13,20,21]. The survey [7] is a good entry point to the literature on geometric and proximity graphs, where for example one draws points at random in the plane and connects points at distance smaller than a given threshold.…”

Section: Introductionmentioning

confidence: 81%

Spatial Gibbs random graphs

Mourrat¹,

Valesin

2018

Ann. Appl. Probab.

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Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with small average graph distance between vertices, but adding an edge comes at a cost measured according to the geometry of the ambient physical space. In most cases, we identify the order of magnitude of the average graph distance as a function of the parameters of the model. As the proofs reveal, hierarchical structures naturally emerge from our simple modeling assumptions. Moreover, a critical regime exhibits an infinite number of discontinuous phase transitions. MSC 2010: 82C22; 05C80

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Section: Introductionmentioning

confidence: 81%

Spatial Gibbs random graphs

Mourrat¹,

Valesin

2018

Ann. Appl. Probab.

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“…We speak of spatially induced clustering. Spatial preferential attachment models were studied by Manna and Sen [22], Flaxman, Frieze and Vera [11,12], Aiello, Bonato, Cooper, Janssen and Pra lat [1], Jordan [17,18], Janssen, Pra lat, Wilson [16], Jordan and Wade [19], and Jacob and Mörters [14,15].…”

Section: Potential Features Of Network We Are Interested In Includementioning

confidence: 99%

The age-dependent random connection model

et al. 2019

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We investigate a class of growing graphs embedded into the d-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on time, their spatial distance and their relative ages. This simple model for a scale-free network is called the age-based spatial preferential attachment network and is based on the idea of preferential attachment with spatially induced clustering. We show that the graphs converge weakly locally to a variant of the random connection model, which we call the age-dependent random connection model. This is a natural infinite graph on a Poisson point process where points are marked by a uniformly distributed age and connected with a probability depending on their spatial distance and both ages. We use the limiting structure to investigate asymptotic degree distribution, clustering coefficients and typical edge lengths in the age-based spatial preferential attachment network.MSc classification (2010): Primary 05C80 Secondary 60K35.

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“…The last decades in stochastic geometry have seen a growing interest in models that deal with random geometric objects evolving in time. As examples we mention random sequential packings [28,33], spatial birth and growth models like the Johnson-Mehl growth process [1,28], the construction of polygonal Markov random fields [30,31,32], falling/dead leaf models [2,3,5], on-line geometric random graphs such as the on-line nearest neighbour graph [27,43] or the geometric preferential attachment graph [7,8,9]. A particularly attractive class of models studied in stochastic geometry is that of random tessellations.…”

Section: Introductionmentioning

confidence: 99%