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Long paths in random Apollonian networks
, 2014
"... We consider the length L(n) of the longest path in a randomly generated Apollonian Network (ApN) An. We show that w.h.p. L(n) ≤ ne − logc n for any constant c < 2/3. 1 ..."
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We consider the length L(n) of the longest path in a randomly generated Apollonian Network (ApN) An. We show that w.h.p. L(n) ≤ ne − logc n for any constant c < 2/3. 1
Randomized rumor spreading in poorly connected smallworld networks
 Distributed Computing (DISC ’14), volume 8784 of Lecture Notes in Computer Science
, 2014
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Diameter and Rumour Spreading in RealWorld Network Models
, 2015
"... The socalled ‘smallworld phenomenon’, observed in many realworld 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 socalled ‘smallworld phenomenon’, observed in many realworld 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,