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We present and study in this paper a simple algorithm that produces so called growing Parallel Random Apollonian Networks (P-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scale-free…

Discrete Mathematics · Computer Science 2009-04-30 Nicolas Bonnel , Pierre-François Marteau , Gildas G. Ménier

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups…

Data Analysis, Statistics and Probability · Physics 2010-07-14 Peter J. Mucha , Thomas Richardson , Kevin Macon , Mason A. Porter , Jukka-Pekka Onnela

Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…

Physics and Society · Physics 2018-05-22 Gang Mei , Nengxiong Xu , Salvatore Cuomo

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Probability · Mathematics 2022-07-19 Ivan Kryven , Rik Versendaal

We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…

Probability · Mathematics 2024-03-05 Sayan Banerjee , Shankar Bhamidi , Xiangying Huang

We find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes. To counteract and measure the effect of superrich nodes, we propose a paradigm to quantify the mixing pattern of a real network in…

Physics and Society · Physics 2015-05-14 Xiao-Ke Xu , Jie Zhang , Junfeng Sun , Michael Small

We investigate three different approaches for fitting the degree distributions of China-, US- and the composite China+US air network, in order to reveal the nature of such distributions and the potential theoretical background on which they…

Physics and Society · Physics 2016-08-16 Wei Li , Qiuping A. Wang , Laurent Nivanen , Alain Le Méhauté

Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…

Physics and Society · Physics 2015-12-03 Snehal M. Shekatkar , G. Ambika

The correlation-based financial networks are studied intensively. However, previous studies ignored the importance of the anti-correlation. This paper is the first to consider the anti-correlation and positive correlation separately, and…

Statistical Finance · Quantitative Finance 2025-10-27 Peng Liu

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…

Dynamical Systems · Mathematics 2016-01-07 Martin Ritchie , Luc Berthouze , Istvan Z. Kiss

In this article, we investigate several properties of high-dimensional random Apollonian networks (HDRANs), including two types of degree profiles, the small-world effect (clustering property), sparsity, and three distance-based metrics.…

Probability · Mathematics 2020-09-28 Panpan Zhang

Observability of complex systems/networks is the focus of this paper, which is shown to be closely related to the concept of contraction. Indeed, for observable network tracking it is necessary/sufficient to have one node in each…

Systems and Control · Computer Science 2017-09-13 Mohammadreza Doostmohammadian , Hamid R. Rabiee , Houman Zarrabi , Usman Khan

The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the…

Statistical Mechanics · Physics 2013-05-29 J. Saramaki , M. Kivela , J. -P. Onnela , K. Kaski , J. Kertesz

We use the emergent field of Complex Networks to analyze the network of scientific collaborations between entities (universities, research organizations, industry related companies,...) which collaborate in the context of the so-called…

Data Analysis, Statistics and Probability · Physics 2009-01-23 Juan A. Almendral , Joao G. Oliveira , L. López , J. F. F. Mendes , Miguel A. F. Sanjuán

Modern information and communication technologies, especially the Internet, have diminished the role of spatial distances and territorial boundaries on the access and transmissibility of information. This has enabled scientists for closer…

Physics and Society · Physics 2012-12-18 Raj Kumar Pan , Kimmo Kaski , Santo Fortunato

In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…

Physics and Society · Physics 2011-10-11 Zou Zhi-Yun , Liu Peng , Lei Li , Gao Jian-Zhi

We applied a mean field approach to study clustering coefficients in Barabasi-Albert networks. We found that the local clustering in BA networks depends on the node degree. Analytic results have been compared to extensive numerical…

Statistical Mechanics · Physics 2016-08-31 Agata Fronczak , Piotr Fronczak , Janusz A. Holyst

Retractions undermine the reliability of scientific literature and the foundation of future research. Analyzing collaboration networks in retracted papers can identify risk factors, such as recurring co-authors or institutions. This study…

Information Retrieval · Computer Science 2024-11-27 Kiran Sharma , Aanchal Sharma , Jazlyn Jose , Vansh Saini , Raghavraj Sobti , Ziya Uddin

Following Henry Small in his approach to co-citation analysis, highly cited sources are seen as concept symbols of research fronts. But instead of co-cited sources I cluster citation links, which are the thematically least heterogenous…

Digital Libraries · Computer Science 2022-01-26 Frank Havemann

Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…