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Spectra Statistics of the Transition Matrices on WattsStrogatz Model
, 2008
"... Spectral properties of the transition matrix of a smallworld network model are studied, and how those properties are relevant to the network structure is elucidated. The distribution of the nearest neighbor eigenvalue spacings changes from a levelcrossing to an avoidedcrossing type as the rewirin ..."
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Spectral properties of the transition matrix of a smallworld network model are studied, and how those properties are relevant to the network structure is elucidated. The distribution of the nearest neighbor eigenvalue spacings changes from a levelcrossing to an avoidedcrossing type
Local edges
"... Six degrees of separation “We are all linked by short chains of acquaintance” WattsStrogatz model Pervasive in networks arising in nature and technology Fundamental factor in the evolution of WWW Kleinberg: People can find short paths very effectively Can we put an algorithmic price on that? ..."
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Six degrees of separation “We are all linked by short chains of acquaintance” WattsStrogatz model Pervasive in networks arising in nature and technology Fundamental factor in the evolution of WWW Kleinberg: People can find short paths very effectively Can we put an algorithmic price on that?
The SmallWorld Phenomenon: An Algorithmic Perspective
 in Proceedings of the 32nd ACM Symposium on Theory of Computing
, 2000
"... Long a matter of folklore, the “smallworld phenomenon ” — the principle that we are all linked by short chains of acquaintances — was inaugurated as an area of experimental study in the social sciences through the pioneering work of Stanley Milgram in the 1960’s. This work was among the first to m ..."
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Cited by 823 (5 self)
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that no decentralized algorithm, operating with local information only, can construct short paths in these networks with nonnegligible probability. We then define an infinite family of network models that naturally generalizes the WattsStrogatz model, and show that for one of these models, there is a decentralized
ASYMPTOTIC SPECTRAL ANALYSIS OF GENERALIZED ERDŐS–RÉNYI RANDOM GRAPHS
"... Abstract. Motivated by the Watts–Strogatz model for a complex network, we introduce a generalization of the Erdős–Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit. 1. Introduction. Since the epochmaking papers by Watts– ..."
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Abstract. Motivated by the Watts–Strogatz model for a complex network, we introduce a generalization of the Erdős–Rényi random graph. We derive a combinatorial formula for the moment sequence of its spectral distribution in the sparse limit. 1. Introduction. Since the epochmaking papers by Watts–Strogatz
WattsStrogatz Graphs Exponential Family Random Graphs Generative Models, Preferential Attachment References
, 2009
"... n nodes, edges are IID binary variables with probability p ..."
Social and Technological Networks Edinburg, 2015 Lecture 5 & 6. Small Worlds Rik Sarkar Class notes
"... • A definition of small world networks • The Watts Strogatz model for small worlds • Kleinberg’s model for small worlds Note that different people tend to have different things in mind when they say small world. The definition we had in class is one I thought reasonable. At the very least, a small w ..."
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• A definition of small world networks • The Watts Strogatz model for small worlds • Kleinberg’s model for small worlds Note that different people tend to have different things in mind when they say small world. The definition we had in class is one I thought reasonable. At the very least, a small
Small worlds, mazes and random walks
, 2002
"... PACS. 05.40.Fb – Random walks and Levy flights. PACS. 02.50.r – Probability theory, stochastic processes, and statistics. PACS. 02.70.Uu – Applications of Monte Carlo methods. Abstract. – A parametrized family of random walks whose trajectories are easily identified as graphs is presented. This con ..."
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model establishes a link between Complex Networks and SelfAvoiding Random Walks, a useful theoretical framework in polymer science. The WattsStrogatz model of Small World graphs [1] efficientlyinterpolates between regular and random graphs thanks to a small number pN of shortcuts (long
On Merging and Dividing Social Graphs
, 2015
"... Abstract Modeling social interaction can be based on graphs. However most models lack the flexibility of including larger changes over time. The BarabásiAlbertmodel is a generative model which already offers mechanisms for adding nodes. We will extent this by presenting four methods for merging a ..."
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as well. All algorithms were tested in multiple experiments using graphs based on the BarabásiAlbertmodel, an extended version of the BarabásiAlbertmodel by Holme and Kim, the WattsStrogatzmodel and the ErdősRényimodel. Furthermore we concluded that our algorithms are able to preserve dif
IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL
, 2007
"... The Watts–Strogatz network model developed by including degree distribution: theory and computer simulation ..."
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The Watts–Strogatz network model developed by including degree distribution: theory and computer simulation
Random Graph Dynamics
, 2007
"... Chapter 1 will explain what this book is about. Here I will explain why I chose to write the book, how it is written, where and when the work was done, and who helped. Why. It would make a good story if I was inspired to write this book by an image of Paul Erdös magically appearing on a cheese ques ..."
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Cited by 203 (2 self)
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model, which inspired me to prove some rigorous results about their model, and (iii) a book review I wrote on the books by Watts and Barabási for the Notices of the American Math Society. The subject of this book was attractive for me, since many of the papers were outside the mathematics literature
Results 1  10
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