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We consider the problem of determining asymptotic bounds on the capacity of a random ad hoc network. Previous approaches assumed a link layer model in which if a transmitter-receiver pair can communicate with each other, i.e., the Signal to…

Information Theory · Computer Science 2008-11-24 Vivek P. Mhatre , Catherine P. Rosenberg , Ravi R. Mazumdar

We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…

Physics and Society · Physics 2026-02-18 V. Adami , S. Emdadi-Mahdimahalleh , H. J. Herrmann , M. N. Najafi

Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…

Physics and Society · Physics 2017-09-11 Philip Tee , Ian Wakeman , George Parisis , Jonathan Dawes , István Z. Kiss

Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…

Statistical Mechanics · Physics 2014-12-03 M. E. J. Newman , Travis Martin

We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…

Statistical Mechanics · Physics 2012-06-01 S. Mehraban , M. R. Ejtehadi

In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…

Disordered Systems and Neural Networks · Physics 2009-11-10 Lazaros K. Gallos

Many real-world networks exhibit the phenomenon of edge clustering, which is typically measured by the average clustering coefficient. Recently, an alternative measure, the average closure coefficient, is proposed to quantify local…

Statistics Theory · Mathematics 2023-12-07 Mingao Yuan

With a simple attack and repair evolution model, we investigate the stability and structural changes of the Erdos-Renyi random graphs (RG) and Barabasi-Albert scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to…

Statistical Mechanics · Physics 2007-05-23 L. P. Chi , C. B. Yang , X. Cai

We consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the…

Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-02-03 Graeme Smith , J. W. Sanders , Qin Li

In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This enables us to enumerate loop-free digraphs and oriented graphs…

Combinatorics · Mathematics 2026-01-09 Catherine Greenhill , Mahdieh Hasheminezhad , Isaiah Iliffe , Brendan D. McKay

Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…

Quantitative Methods · Quantitative Biology 2017-02-07 John Lang , Hans De Sterck , Jamieson L. Kaiser , Joel C. Miller

Randomly sampling an acyclic orientation on the complete bipartite graph $K_{n,k}$ with parts of size $n$ and $k$, we investigate the length of the longest path. We provide a probability generating function for the distribution of the…

Combinatorics · Mathematics 2024-08-26 Jessica Khera , Erik Lundberg

In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is…

Physics and Society · Physics 2017-05-05 Yi-Min Ding , Jun Meng , Jing-Fang Fan , Fang-Fu Ye , Xiao-Song Chen

The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…

Disordered Systems and Neural Networks · Physics 2013-05-29 Aaron Clauset , Cristopher Moore

In this paper, we propose a network whose nodes are labeled by the composite numbers and two nodes are connected by an undirected link if they are relatively prime to each other. As the size of the network increases, the network will be…

Combinatorics · Mathematics 2024-07-22 Md Rahil Miraj , Dibakar Ghosh , Chittaranjan Hens

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…

Statistical Mechanics · Physics 2009-11-07 Illes J. Farkas , Imre Derenyi , Albert-Laszlo Barabasi , Tamas Vicsek

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…

Physics and Society · Physics 2011-11-09 Zhongzhi Zhang , Shuigeng Zhou , Lichao Chen , Jihong Guan , Lujun Fang , Yichao Zhang

We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index $\alpha\in(1,2)$. When the number $n$ of…

Probability · Mathematics 2017-08-23 Jean-François Le Gall , Grégory Miermont

We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…

Information Theory · Computer Science 2022-06-24 Mihai-Alin Badiu , Justin P. Coon