Random intersection graphs whenm=?(n): An equivalence theorem relating the evolution of theG(n,m,p) andG(n,p) models

Fill, James Allen; Scheinerman, Edward R.; Singer-Cohen, Karen B.

doi:10.1002/(sici)1098-2418(200003)16:2<156::aid-rsa3>3.0.co;2-h

Cited by 79 publications

(1 citation statement)

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“…Note however that there are also several popular models that cannot be expressed in terms of a sequence Gn (W, t) for any kernel W , such as percolation on sparse graphs or random intersection graphs (see [6,9,11,14] for some connectivity results about those models).…”

Section: Introduction and Model Descriptionmentioning

confidence: 99%

Connectivity of Poissonian inhomogeneous random multigraphs

Federico

2023

EJGTA

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We introduce a model for inhomogeneous random graphs designed to have a lot of flexibility in the assignment of the degree sequence and the individual edge probabilities while remaining tractable. To achieve this we run a Poisson point process over the square [0, 1] 2 , with an intensity proportional to a kernel W (x, y) and identify every couple of vertices of the graph with a subset of the square, adding an edge between them if there is a point in such subset. This ensures unconditional independence among edges and makes many statements much easier to prove in this setting than in other similar models. Here we prove sharpness of the connectivity threshold under mild integrability conditions on W (x, y).

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Section: Introduction and Model Descriptionmentioning

confidence: 99%

Connectivity of Poissonian inhomogeneous random multigraphs

Federico

2023

EJGTA

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Component evolution in a secure wireless sensor network

2008

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We study a connectivity property of a secure wireless network that uses random pre-distribution of keys. A network is composed of n sensors. Each sensor is assigned a collection of d different keys drawn uniformly at random from a given set of m keys. Two sensors are joined by a communication link if they share a common key. We show that for large n with high probability the connected component of size (n) emerges in the network when the probability of a link exceeds the threshold 1/n. Similar component evolution is shown for networks where sensors communicate if they share at least s common keys.

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