By Reuven Cohen

Studying very important effects and analytical suggestions, this graduate-level textbook is a step by step presentation of the constitution and serve as of complicated networks. utilizing quite a number examples, from the soundness of the web to effective equipment of immunizing populations, and from epidemic spreading to how one may well successfully look for members, this textbook explains the theoretical equipment that may be used, and the experimental and analytical effects received within the research and learn of advanced networks. Giving specified derivations of many ends up in complicated networks conception, this is often an amazing textual content for use through graduate scholars getting into the sphere. End-of-chapter assessment questions support scholars visual display unit their very own realizing of the fabrics awarded.

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**Additional info for Complex Networks: Structure, Robustness and Function**

**Sample text**

4 Introducing correlations A final static model discussed here is networks with a given degree sequence and correlations. 5. The most general form of degree-degree correlations is obtained by having a probability density function P(k1 , k2 ), which is the probability of having a link between a node of degree k1 and a node of degree k2 . In order to be consistent, P(k1 , k2 ) should be symmetric and k1 and k2 (for undirected graphs) should satisfy the equality k2 P(k1 , k2 ) = P(k1 )k1 /N . Equivalently, one may use the conditional probability density P(k2 |k1 ), which is the probability of reaching a node having degree k2 by a link emanating from a node of a given degree k1 .

Observed in many real-world networks. This led Watts and Strogatz to develop an alternative model, called the “small-world” model [WS98]. 2). For each site, each of the links emanating from it is removed with probability ϕ and is rewired to a randomly selected site in the network. A variant of this process is to add links rather than rewire, which simplifies the analysis without considerably affecting the results. 2 Introducing shortcuts: small-world networks of both an ordered lattice (large clustering) and a random network (small world), as we will discuss below.

As a guiding principle for the construction of embedded networks in general, we impose the natural restriction that the total geometrical length of links in the system be minimal. Several other models have been suggested, for instance, in 42 Models for complex networks [MS02, WSS02b]. Some of these models, such as [MS02], place the nodes not on a lattice, but on randomly selected points in Euclidean space. Other models, such as [WSS02b], allow deviations from the degree distribution in the low-degree regime.