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On Certain Properties of Random Apollonian Networks
"... In this work we analyze fundamental properties of Random Apollonian Networks [34,35], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the dia ..."
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In this work we analyze fundamental properties of Random Apollonian Networks [34,35], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the diameter, where k is a constant.
Randomized rumor spreading in poorly connected small-world networks
- Distributed Computing (DISC ’14), volume 8784 of Lecture Notes in Computer Science
, 2014
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A new model for a Scale-free . . .
, 2011
"... Scale-free networks are usually defined as the ones that have power law degree distributions. Since many of real world networks such as the World Wide Web, the Internet, citation networks, biological networks, and so on, have this property in common, scale-free networks have attracted interests of r ..."
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Scale-free networks are usually defined as the ones that have power law degree distributions. Since many of real world networks such as the World Wide Web, the Internet, citation networks, biological networks, and so on, have this property in common, scale-free networks have attracted interests of researchers so far. They also revealed that such networks have some typical properties such as high cluster coefficient and small diameter as well, and a lot of network models have been proposed to explain those properties. Recently, it is reported that the following new properties about self-similar structures of a real world network are observed [Uno and Oguri, FAW and AAIM, 2011]. For a special kind of cliques in a network, 1. the size distributions of these cliques show a power-law, 2. the degree distribution of the network after contracting these cliques show a power-law, and 3. by regarding the contracted network as the original, 1 and 2 are observed repeatedly. In this paper, we propose a new network model constructed by a ‘clique expansion’ procedure, and show that it can explain this ‘hierarchical structure of cliques’.
Some Properties of Random Apollonian Networks
"... In this work we analyze fundamental properties of Random Apollonian Networks [37,38], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the diam ..."
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In this work we analyze fundamental properties of Random Apollonian Networks [37,38], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the diameter, where k is a constant.
THE DEGREE SEQUENCE OF RANDOM APOLLONIAN NETWORKS
"... Abstract. We analyze the asymptotic behavior of the degree sequence of Random Apollonian Networks [11]. For previous weaker results see [10, 11]. 1. ..."
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Abstract. We analyze the asymptotic behavior of the degree sequence of Random Apollonian Networks [11]. For previous weaker results see [10, 11]. 1.
Diameter and Rumour Spreading in Real-World Network Models
, 2015
"... The so-called ‘small-world phenomenon’, observed in many real-world networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network’s size, typically growing as a logarithmic function. Several mathematical models have been defined for socia ..."
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The so-called ‘small-world phenomenon’, observed in many real-world networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network’s size, typically growing as a logarithmic function. Several mathematical models have been defined for social networks, the WWW, etc., and this phenomenon translates to proving that such models have a small diameter. In the first part of this thesis, we rigorously analyze the diameters of several random graph classes that are introduced specifically to model complex networks, verifying whether this phenomenon occurs in them. In Chapter 3 we develop a versatile technique for proving upper bounds for diameters of evolving random graph models, which is based on defining a coupling between these models and variants of random recursive trees. Using this technique we prove, for the first time,
