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# 数据科学代写|复杂网络代写Complex Network代考|CS60078 Berezinskii-Kosterlitz

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## 数据科学代写|复杂网络代写Complex Network代考|Berezinskii-Kosterlitz

The models of growing networks of the preceding sections generated connected random graphs. In general, growing networks can contain a set of connected components. How does a giant connected component emerge in such growing networks? Callaway, Hopcroft, Kleinberg, Newman, and Strogatz (2001) studied the birth of a giant connected component in growing networks and discovered a phase transition, quite distinct from the one in equilibrium networks. They considered the following model:

At each time step, a new vertex is added to a network.

Simultaneously, $b$ new undirected edges emerge between pairs of uniformly randomly chosen vertices ( $b$ may be non-integer).

## 数据科学代写|复杂网络代写Complex Network代考|Accelerated growth and densification

In many real networks the number of edges grows faster than the number of vertices, so that the average degree of a vertex is a growing function of the network size – connections become more dense (Leskovec, Kleinberg, and Faloutsos, 2007b). ${ }^{18}$ This non-linear, or, one can say, ‘accelerated’, growth has numerous consequences (Dorogovtsev and Mendes, 2001a, 2003). For example, the diameter of a growing network of this kind may be constant or even shrink as the number of vertices increases. The models of networks that we have considered up to now do not show this accelerated growth. It is not very difficult, however, to incorporate this feature into network models
${ }^{17}$ The reader will find the details of these calculations in Dorogovtsev, Mendes, and Samukhin (2001a).
${ }^{18}$ Broder, Kumar, Maghoul, Raghavan, Rajagopalan, Stata, Tomkins, and Wiener (2000) first measured the density of connections in the WWW in May 1999 and found that the average in- and out-degrees of a vertex are equal at 7.22. When they repeated the measurements in October 1999, the average in- and out-degrees were already $7.85$.

## 数据科学代写|复杂网络代写Complex Network代考|Accelerated growth and densification

17读者将在 Dorogovtsev、Mendes 和 Samukhin (2001a) 中找到这些计算的详细信息。
18Broder、Kumar、Maghoul、Raghavan、Rajagopalan、Stata、Tomkins 和 Wiener (2000) 于 1999 年 5 月首次测量了 WWW 中的连接密度，发现顶点的平均入度和出度相等，为 7.22。当他们在 1999 年 10 月重复测量时，平均入度和出度已经7.85.

## MATLAB代写

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