Limiting Properties of Random Graph Models with Vertex and Edge Weights

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Limiting Properties of Random Graph Models with Vertex and Edge Weights. / Foss, Sergey; Konstantopoulos, Takis.

In: Journal of Statistical Physics, Vol. 173, No. 3-4, 01.11.2018, p. 626-643.

Research output: Contribution to journal › Article › peer-review

Harvard

Foss, S & Konstantopoulos, T 2018, 'Limiting Properties of Random Graph Models with Vertex and Edge Weights', Journal of Statistical Physics, vol. 173, no. 3-4, pp. 626-643. https://doi.org/10.1007/s10955-018-2080-3

APA

Foss, S., & Konstantopoulos, T. (2018). Limiting Properties of Random Graph Models with Vertex and Edge Weights. Journal of Statistical Physics, 173(3-4), 626-643. https://doi.org/10.1007/s10955-018-2080-3

Vancouver

Foss S, Konstantopoulos T. Limiting Properties of Random Graph Models with Vertex and Edge Weights. Journal of Statistical Physics. 2018 Nov 1;173(3-4):626-643. doi: 10.1007/s10955-018-2080-3

Author

Foss, Sergey ; Konstantopoulos, Takis. / Limiting Properties of Random Graph Models with Vertex and Edge Weights. In: Journal of Statistical Physics. 2018 ; Vol. 173, No. 3-4. pp. 626-643.

BibTeX

@article{c86aeabd207f421984d03f4a672d4be3,

title = "Limiting Properties of Random Graph Models with Vertex and Edge Weights",

abstract = "This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on edges and vertices and assuming that weights on edges are signed. We aim at an exposition that summarizes, simplifies, and extends proof ideas. We also study sparse graph asymptotics, showing convergence of the weighted random graphs to a certain weighted graph that can be constructed in terms of Poisson processes. We are motivated by numerous applications, ranging from ecology to parallel computing models. It is the latter set of applications that necessitates the introduction of vertex weights. Finally, we discuss some open problems and research directions.",

keywords = "Limit theorems, Random graphs, Stochastic networks, CONVERGENCE, LEVEL-SPACING DISTRIBUTIONS",

author = "Sergey Foss and Takis Konstantopoulos",

note = "Publisher Copyright: {\textcopyright} 2018, The Author(s).",

year = "2018",

month = nov,

day = "1",

doi = "10.1007/s10955-018-2080-3",

language = "English",

volume = "173",

pages = "626--643",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "3-4",

}

RIS

TY - JOUR

T1 - Limiting Properties of Random Graph Models with Vertex and Edge Weights

AU - Foss, Sergey

AU - Konstantopoulos, Takis

PY - 2018/11/1

Y1 - 2018/11/1

N2 - This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on edges and vertices and assuming that weights on edges are signed. We aim at an exposition that summarizes, simplifies, and extends proof ideas. We also study sparse graph asymptotics, showing convergence of the weighted random graphs to a certain weighted graph that can be constructed in terms of Poisson processes. We are motivated by numerous applications, ranging from ecology to parallel computing models. It is the latter set of applications that necessitates the introduction of vertex weights. Finally, we discuss some open problems and research directions.

AB - This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on edges and vertices and assuming that weights on edges are signed. We aim at an exposition that summarizes, simplifies, and extends proof ideas. We also study sparse graph asymptotics, showing convergence of the weighted random graphs to a certain weighted graph that can be constructed in terms of Poisson processes. We are motivated by numerous applications, ranging from ecology to parallel computing models. It is the latter set of applications that necessitates the introduction of vertex weights. Finally, we discuss some open problems and research directions.

KW - Limit theorems

KW - Random graphs

KW - Stochastic networks

KW - CONVERGENCE

KW - LEVEL-SPACING DISTRIBUTIONS

UR - http://www.scopus.com/inward/record.url?scp=85049585076&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-2080-3

DO - 10.1007/s10955-018-2080-3

M3 - Article

AN - SCOPUS:85049585076

VL - 173

SP - 626

EP - 643

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -

ID: 14405759