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Modern social networks frequently encompass multiple distinct types of connectivity information; for instance, explicitly acknowledged friend relationships might complement behavioral measures that link users according to their actions or…

Social and Information Networks · Computer Science 2015-06-17 Brandon Oselio , Alex Kulesza , Alfred O. Hero

We introduce a new percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the…

Probability · Mathematics 2010-03-30 Ronald Meester , Pieter Trapman

We consider the problem of recovering latent information from graphs under $\varepsilon$-edge local differential privacy where the presence of relationships/edges between two users/vertices remains confidential, even from the data curator.…

Machine Learning · Computer Science 2025-04-25 Siddharth Vishwanath , Jonathan Hehir

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

Physics and Society · Physics 2018-03-21 Zexun Wang , Dong Zhou , Yanqing Hu

In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…

Combinatorics · Mathematics 2009-02-03 Laszlo Lovasz

We study fundamental characteristics for the connectivity of multi-hop D2D networks. Devices are randomly distributed on street systems and are able to communicate with each other whenever their separation is smaller than some connectivity…

Networking and Internet Architecture · Computer Science 2018-02-01 Elie Cali , Nila Novita Gafur , Christian Hirsch , Benedikt Jahnel , Taoufik En-Najjary , Robert I. A. Patterson

We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…

Statistical Mechanics · Physics 2014-11-20 Brian Karrer , M. E. J. Newman , Lenka Zdeborová

Consider a stationary Poisson process $\eta$ in the $d$-dimensional Euclidean or hyperbolic space and construct a random graph with vertex set $\eta$ as follows. First, each point $x\in\eta$ is connected by an edge to its nearest neighbour,…

Probability · Mathematics 2024-11-04 Holger Sambale , Christoph Thäle , Tara Trauthwein

In the presented article, statistical properties regarding the topology and standard percolation on relative neighborhood graphs (RNGs) for planar sets of points, considering the Euclidean metric, are put under scrutiny. RNGs belong to the…

Statistical Mechanics · Physics 2013-04-17 O. Melchert

Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…

Physics and Society · Physics 2016-03-30 Filippo Radicchi , Claudio Castellano

Keeler, Ross and Xia (2016) recently derived approximation and convergence results, which imply that the point process formed from the signal strengths received by an observer in a wireless network under a general statistical propagation…

Networking and Internet Architecture · Computer Science 2016-11-09 Paul Keeler , Nathan Ross , Aihua Xia , Bartlomiej Blaszczyszyn

Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…

Probability · Mathematics 2022-11-03 Nils Detering , Jimin Lin

Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…

Disordered Systems and Neural Networks · Physics 2021-10-04 Łukasz G. Gajewski , Julian Sienkiewicz , Janusz A. Hołyst

Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimised for…

Computational Physics · Physics 2025-04-14 D. A. Head

In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We…

Discrete Mathematics · Computer Science 2007-05-23 Josep Diaz , Dieter Mitsche , Xavier Perez

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Combinatorics · Mathematics 2018-10-11 Mattia G. Bergomi , Massimo Ferri , Lorenzo Zuffi

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

Methodology · Statistics 2011-07-15 Nanny Wermuth

We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean…

Probability · Mathematics 2024-04-19 Peter Gracar , Arne Grauer

Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…

Signal Processing · Electrical Eng. & Systems 2019-05-22 Gonzalo Mateos , Santiago Segarra , Antonio G. Marques , Alejandro Ribeiro

We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…

Physics and Society · Physics 2014-04-18 Sergey Melnik , Mason A. Porter , Peter J. Mucha , James P. Gleeson