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Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.


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TL;DR: In this article, the authors provide a framework for determining the centrality of agents in a broad family of random networks, and illustrate the economic consequences of these results by presenting three applications: (1) in network formation models based on community structure (called stochastic block models), they show network segregation and differences in community size produce inequality.
Abstract: We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random network models to accommodate data limitations or prove asymptotic results. Our main theorems show that on large random networks, centrality measures are close to their expected values with high probability. We illustrate the economic consequences of these results by presenting three applications: (1) In network formation models based on community structure (called stochastic block models), we show network segregation and differences in community size produce inequality. Benefits from peer effects tend to accrue disproportionately to bigger and better-connected communities. (2) When link probabilities depend on geography, we can compute and compare the centralities of agents in different locations. (3) In models where connections depend on several independent characteristics, we give a formula that determines centralities 'characteristic-by-characteristic'. The basic techniques from these applications, which use the main theorems to reduce questions about random networks to deterministic calculations, extend to many network games.

4 citations

Book ChapterDOI
05 Feb 2015
TL;DR: A new model called k-degree closeness anonymization is proposed by adopting a mixed strategy of k- degree anonymity, degree centrality and closeness centrality, which can be used to identify a social entity in the presence of kdegree anonymization.
Abstract: Social network data are generally published in the form of social graphs which are being used for extensive scientific research. We have noticed that even a k-degree anonymization of social graph can't ensure protection against identity disclosure. In this paper, we have discussed how closeness centrality measure can be used to identify a social entity in the presence of kdegree anonymization. We have proposed a new model called k-degree closeness anonymization by adopting a mixed strategy of k-degree anonymity, degree centrality and closeness centrality. The model has two phases, namely, construction and validation. The construction phase transforms a graph with given sequence to a graph with anonymous sequence in such a manner that the closeness centrality measure is distributed among the nodes in a smooth way. The nodes with the same degree centrality are assigned with a closer set of closeness centrality values, making re-identification difficult. Validation phase validates our model by generating 1-neighborhood graphs. Algorithms have been developed both for the construction and validation phases.

4 citations

Journal ArticleDOI
TL;DR: In this paper, the cascade capacity is used to measure how "choosy" individuals in a social network can be and still allow an individual to cause something to spread completely through the network.
Abstract: Why ideas and practices spread an important topic for management scholars and practitioners. This paper presents the cascade capacity as an aspect of network structure as a measure of essentially how ‘choosy’ everyone in a social network can be and still allow an individual to cause something to spread completely through the network. Drawing on social contagion theory and network theory, we propose a research model about how network structure relates to diffusion and test it by simulation, using network data from the popular microblogging service Twitter. Results show the cascade capacity is an important determinant of diffusion, even when we model for homophily. We show how the concept could be used to select individuals to seed to encourage word of mouth marketing. Copyright © 2016 John Wiley & Sons, Ltd.

4 citations

Journal ArticleDOI
TL;DR: The present issue of Focus on Complex Networked Systems has collected contributions from scientists at the very forefront of the theory and applications of complex networks, and consists of identifying the unifying principles and statistical properties that are common to most real networks and how these can be captured via network generation models and algorithms.
Abstract: Complex networks are becoming manifest in many fields of contemporary science, including mathematics, physics, computer science, biology, engineering, social sciences and economics. As part of a broad movement towards research in complex systems, scientists have recently found a striking degree of self-organization that emerges in networks representing seemingly diverse complex systems (Barabasi A L 2005 Nat. Phys. 1 68). The research subject of complex networks comprises the study of how networks emerge and evolve, what is their topology, how robust they are, what new phenomena emerge as a result of the interplay between the structure and dynamics and how can we take advantage of this knowledge for applications in a wide range of natural and man-made systems. The challenge is to understand and accurately model the structure of complex networks to get more insight and a better understanding of their complex topology and functional behavior, since both are intimately linked. This makes the network approach particularly suitable to explore important aspects of complexity. The last decade has witnessed a burst of research activity in the study of large systems made of many non-identical entities, whose interaction or interconnection patterns show complex network-like structures. The research community has benefited from the massive and comparative analysis of networks from different fields, which has produced a series of unexpected results and has shown that previous models proposed in mathematical graph theory are very far from reality (see e.g., Newman M E J 2003 SIAM Rev. 45 167, Boccaletti S et al 2006 Phys. Rep. 424 175). Broadly speaking, research on such complex networks has found its focus in several directions. The first direction of research deals with the structure of networks and consists of identifying the unifying principles and statistical properties that are common to most real networks and how these can be captured via network generation models and algorithms. Another important body of work deals with spreading and percolation-like processes in complex networks, addressing a variety of phenomena ranging from disease spreading to information flow and resilience to random failures and attacks. A third and promising branch of research has arisen in the last few years spurred by the new insights gained through network modeling. It has to do with the study of the behavior of large assemblies of dynamical and nonlinear systems interacting via complex topologies. Phenomena such as synchronization, the emergence of cooperation in social and biological systems, as well as signaling and gene regulatory dynamics and other biochemical processes are now being tackled with a fresh viewpoint by considering both sources of entangled complexity: the structure and the dynamics of the system's constituents. Finally, due to adaptive and dynamical wiring, networks are also dynamical entities, whose topologies evolve and adapt in time. This is another field of research which is just emerging with promising applications to a number of areas including wireless communication systems and brain dynamics. Though modern network theory has produced a number of relevant results in the last few years, it is still at an early stage, particularly when it comes to applications in real systems and to the comprehension of the relation between their structure and function (dynamics). The subject of complex networks is highly interdisciplinary and physicists are making important contributions to the theory, with applications to areas as diverse as computer science, mathematical epidemiology, social and biological sciences, etc. This spirit is reflected in the present issue, which has collected contributions from scientists at the very forefront of the theory and applications of complex networks. The articles that make up this Focus Issue are only examples of the wide range of topics that are explored using the tools developed during the last few years. Although important progress has been made during the last decade, our understanding of complex networked systems, their structure and dynamics, is still far from well-established. We hope that this Focus Issue will further contribute towards better understanding of complex systems. The articles below represent the first contributions and further additions will appear. Focus on Complex Networked Systems: Theory and Applications Contents Beyond centrality—classifying topological significance using backup efficiency and alternative paths Yuval Shavitt and Yaron Singer Scatter networks: a new approach for analysing information scatter Lada A Adamic, K Suresh and Xiaolin Shi New approaches to model and study social networks P G Lind and H J Herrmann Search in spatial scale-free networks H P Thadakamalla, R Albert and S R T Kumara Worm epidemics in wireless ad hoc networks Maziar Nekovee A measure of centrality based on network efficiency V Latora and M Marchiori Dynamical and spectral properties of complex networks Juan A Almendral and Albert Diaz-Guilera Directed network modules Gergely Palla, Illes J Farkas, Peter Pollner, Imre Derenyi and Tamas Vicsek Topology control with IPD network creation games Jan C Scholz and Martin O W Greiner Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks J Poncela, J Gomez-Gardenes, L M Floria and Y Moreno The interplay of universities and industry through the FP5 network Juan A Almendral, J G Oliveira, L Lopez, Miguel A F Sanjuan and J F F Mendes Bounding network spectra for network design Adilson E Motter Accelerating networks David M D Smith, Jukka-Pekka Onnela and Neil F Johnson Weighted network modules Illes Farkas, Daniel Abel, Gergely Palla and Tamas Vicsek Analysis of a large-scale weighted network of one-to-one human communication Jukka-Pekka Onnela, Jari Saramaki, Jorkki Hyvonen, Gabor Szabo, M Argollo de Menezes, Kimmo Kaski, Albert-Laszlo Barabasi and Janos Kertesz Structure–function relationship in complex brain networks expressed by hierarchical synchronization Changsong Zhou, Lucia Zemanova, Gorka Zamora-Lopez, Claus C Hilgetag and Jurgen Kurths Fractality and self-similarity in scale-free networks J S Kim, K-I Goh, B Kahng and D Kim Size reduction of complex networks preserving modularity A Arenas, J Duch, A Fernandez and S Gomez Fractal and transfractal recursive scale-free nets Hernan D Rozenfeld, Shlomo Havlin and Daniel ben-Avraham Building catastrophes: networks designed to fail by avalanche-like breakdown M Woolf, Z Huang and R J Mondragon Structural constraints in complex networks S Zhou and R J Mondragon The complex network of musical tastes Javier M Buldu, P Cano, M Koppenberger, Juan A Almendral and S Boccaletti Shlomo Havlin, Bar-Ilan University, Ramat-Gan, Israel Maziar Nekovee, BT Research, Martlesham, Suffolk, UK and Centre for Computational Science, University College London, UK Yamir Moreno, Institute BIFI, University of Zaragoza, Spain

4 citations

01 Jan 2012
TL;DR: This work examines a variety of models covering the intersection of spreading processes and complex network theory, and although they study a large range of problem formulations, it is found that–surprisingly–a single parameter effectively summarizes the topology.
Abstract: The interactions between people, technology and modern communication paradigms form large and complex human--machine networks Complex network theory attempts to address the global and local behavior of such network structures Of particular interest within the area of network theory is understanding the dynamic behavior of spreading processes on complex networks In this work, we examine a variety of models covering the intersection of spreading processes and complex network theory, and although we study a large range of problem formulations, we find that–surprisingly–a single parameter effectively summarizes the topology We begin by examining the effect that topology has on spreading processes in dynamic networks Dynamic networks are becoming more common due to our increased reliance on and the functionality of mobile devices, smartphones, etc Specifically, we ask, given discrete information spread through a proximity-based communication channel across dynamic network of mobile end-users, what criteria is required such that the information will ultimately die-out; that is, can we determine the tipping point between information survival and die-out? We show analytically that yes, such a threshold exists, yet it is computationally infeasible to calculate To avoid such computationally intensive methods, we go on to provide two approximation methods for determining the tipping point Next, we analyze the effect of topology on the propagation of competing information Using a novel graph structure we refer to as a composite network, we model the intertwined propagation of competing information across a variety of underlying network layers Through a combination of analytical and empirical methods, we show how the topology affects the competing information, and ultimately, using topology, we predict the winner of competition Building on the success of the previous analyses, we formulate a model describing the spread of non-categorical information Unlike our previous models, the information in this system is represented by a continuous value We determine the phase transitions of the overall system, relate them to the tipping points in our previous models, and show both analytically and empirically how the structure of the network affects those phase transitions Ultimately, for each of these models, a single topological parameter, the largest eigenvalue of the adjacency matrix λA ,1, is all that is necessary to characterize the effect of topology on the spreading process

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202240
202175
2020109
201989
2018115