High Degree Vertices and Spread of Infections in Spatially Modelled Social Networks

Feldman, Joshua; Janssen, Jeannette

doi:10.1007/978-3-319-67810-8_5

Cited by 2 publications

(4 citation statements)

References 17 publications

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“…So ε ≥ 5 d −1 log n. Therefore, the probability that (12) fails for a given T ≤ t ≤ 2T is at most 2 exp(−(25/3) log n) = o(n −7 ). Hence, (12) fails for some T ≤ t ≤ 2T with probability o(n −6 ) and the proof is finished. Now, with Lemma 6.2 in hand we can get Theorem 4.1.…”

Section: Simulationsmentioning

confidence: 87%

“…For instance, the SPA model was used to analyze a duopoly market on which there is uncertainty of a product quality [20] and to model the interpersonal network of top managers [23]. Also, [12] used the SPA model to study the interaction between community structure and the spread of infections in complex networks. Fitting the SPA model to real-world networks can also potentially be used for link prediction problems.…”

Section: Properties and Applications Of The Modelmentioning

confidence: 99%

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Local clustering coefficient of spatial preferential attachment model

Iskhakov

Kamiński

Mironov

et al. 2019

Journal of Complex Networks

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In this paper, we study the clustering properties of the Spatial Preferential Attachment (SPA) model. This model naturally combines geometry and preferential attachment using the notion of spheres of influence. It was previously shown in several research papers that graphs generated by the SPA model are similar to real-world networks in many aspects. Also, this model was successfully used for several practical applications. However, the clustering properties of the SPA model were not fully analyzed. The clustering coefficient is an important characteristic of complex networks which is tightly connected with its community structure. In the current paper, we study the behaviour of C(d), which is the average local clustering coefficient for the vertices of degree d. It was empirically shown that in real-world networks C(d) usually decreases as d −a for some a > 0 and it was often observed that a = 1. We prove that in the SPA model C(d) decreases as 1/d. Furthermore, we are also able to prove that not only the average but the individual local clustering coefficient of a vertex v of degree d behaves as 1/d if d is large enough. The obtained results further confirm the suitability of the SPA model for fitting various real-world complex networks.

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Section: Simulationsmentioning

confidence: 87%

Section: Properties and Applications Of The Modelmentioning

confidence: 99%

Local clustering coefficient of spatial preferential attachment model

Iskhakov

Kamiński

Mironov

et al. 2019

Journal of Complex Networks

View full text Add to dashboard Cite

show abstract

“…Further, one-dependent processes in general (beyond FPP) allow for more realistic modelling of real phenomena. In social networks, actual contacts do not scale linearly with the degree due to limited time or awareness [20]. 1-FPP type penalisation has been used to model the sublinear impact of superspreaders as a function of contacts [22,35,40].…”

Section: Discussionmentioning

confidence: 99%

“…The choice of degree-dependent transmission times is not just motivated by the related work mentioned above, but comes directly from applications. Actual contacts do not scale linearly with network connectivity due to limited time or awareness [22], and this type of penalty has been used to model the sublinear impact of superspreaders as a function of contacts [25,31,39].…”

Section: -Fpp Parameters Behaviour Of 1-fpp Transmission Timesmentioning

confidence: 99%

Penalising transmission to hubs in scale-free spatial random graphs

Komjáthy¹,

Lapinskas²,

Lengler³

2021

Ann. Inst. H. Poincaré Probab. Statist.

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In this paper we study a version of (non-Markovian) first passage percolation on graphs, where the transmission time between two connected vertices is non-iid, but increases by a penalty factor polynomial in their expected degrees. Based on the exponent of the penalty-polynomial, this makes it increasingly harder to transmit to and from high-degree vertices. This choice is motivated by awareness or time-limitations. For the iid part of the transmission times we allow any nonnegative distribution with regularly varying behaviour at 0. For the underlying graph models we choose spatial random graphs that have power-law degree distributions, so that the effect of the penalisation becomes visible: (finite and infinite) Geometric Inhomogeneous Random Graphs, and Scale-Free Percolation. In these spatial models, the connection probability between two vertices depends on their spatial distance and on their expected degrees. We prove that upon increasing the penalty exponent, the transmission time between two far away vertices x, y sweeps through four universal phases even for a single underlying graph: explosive (tight transmission times), polylogarithmic, polynomial but sublinear (Θ(|x − y| η0 ) for an explicit η 0 < 1), and linear (Θ(|x − y|)) in their Euclidean distance. Further, none of these phases are restricted to phase boundaries, and those are non-trivial in the main model parameters: the tail of the degree-distribution, a long-range parameter, and the exponent of regular variation of the iid part of the transmission times. In this paper we present proofs of lower bounds for the latter two phases and the upper bound for the linear phase. These complement the matching upper bounds for the polynomial regime in our companion paper.

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High Degree Vertices and Spread of Infections in Spatially Modelled Social Networks

Cited by 2 publications

References 17 publications

Local clustering coefficient of spatial preferential attachment model

Local clustering coefficient of spatial preferential attachment model

Penalising transmission to hubs in scale-free spatial random graphs

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