By Guido Caldarelli
This booklet is the fruits of 3 years of analysis attempt on a multidisciplinary undertaking during which physicists, mathematicians, machine scientists and social scientists labored jointly to reach at a unifying photo of complicated networks. The contributed chapters shape a reference for some of the difficulties in facts research visualization and modeling of complicated networks.
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Additional resources for Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science (Complex Systems and Interdisciplinary Science)
We prompt the interested reader who is willing to work on networks to refer to the above mentioned reviews and to perform extensive literature searches. The two principal classes of models that we are going to describe in the following are static random networks and evolving random networks. Static random networks ought to describe structures where the number of vertices is ﬁxed in time and edges connecting them are assigned according to some probabilistic law once and for all. Whether such networks could describe any real instances is debatable, and yet they clearly represent both a mathematical reference and a tool to create networks satisfying some speciﬁc topological properties.
If the underlying network is Markovian, the stochastic process constructed from the sequence of degrees of the visited vertices follows a Markovian jump process with a transition probability given by P (k|k ) and a steady state distribution given by kP (k)/ k . 3. Empirical measurement of correlations At the level of two vertices degree correlations, the most straightforward measure consists in a direct inspection of the two-dimensional histograms of the joint degree distribution P (k , k)46,47 or the conditional probability P (k | k).
29,30 The duplication procedure is then followed by some tailoring of the page to suit the interests of the owner of the new page, and as a consequence some old hyperlinks can be lost and some new ones acquired. 31,32 As cells divide and organisms reproduce, the duplication of their DNA is accompanied by mutations. Mutations can sometimes entail the complete duplication of a gene. Since in this case the corresponding protein can be produced by two diﬀerent copies of the same gene, point-like mutations on one of them can accumulate at a rate faster than normal since a weaker selection pressure is applied.
Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science (Complex Systems and Interdisciplinary Science) by Guido Caldarelli