Accelerated growth of networks

Dorogovtsev, S. N.; Mendes, J. F. F.

doi:10.1002/3527602755.ch14

Cited by 31 publications

(34 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An observation similar to the findings of Leskovec et al concerning network densification was also previously made by Dorogovtsev and Mendes [4]. They empirically observed that the graph formed by the World Wide Web was densifying over time, naming this phenomenon accelerated growth.…”

Section: Related Worksupporting

confidence: 74%

Densification arising from sampling fixed graphs

Pedarsani

Figueiredo

Grossglauser

2008

Proceedings of the 2008 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems

View full text Add to dashboard Cite

During the past decade, a number of different studies have identified several peculiar properties of networks that arise from a diverse universe, ranging from social to computer networks. A recently observed feature is known as network densification, which occurs when the number of edges grows much faster than the number of nodes, as the network evolves over time. This surprising phenomenon has been empirically validated in a variety of networks that emerge in the real world and mathematical models have been recently proposed to explain it. Leveraging on how real data is usually gathered and used, we propose a new model called Edge Sampling to explain how densification can arise. Our model is innovative, as we consider a fixed underlying graph and a process that discovers this graph by probabilistically sampling its edges. We show that this model possesses several interesting features, in particular, that edges and nodes discovered can exhibit densification. Moreover, when the node degree of the fixed underlying graph follows a heavy-tailed distribution, we show that the Edge Sampling model can yield power law densification, establishing an approximate relationship between the degree exponent and the densification exponent. The theoretical findings are supported by numerical evaluations of the model. Finally, we apply our model to real network data to evaluate its performance on capturing the previously observed densification. Our results indicate that edge sampling is indeed a plausible alternative explanation for the densification phenomenon that has been recently observed.

show abstract

Section: Related Worksupporting

confidence: 74%

Densification arising from sampling fixed graphs

Pedarsani

Figueiredo

Grossglauser

2008

Proceedings of the 2008 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems

View full text Add to dashboard Cite

show abstract

“…We note that this backward approach is also considered in [19]. The results of [12,13,14] correspond to those of this paper as follows: For the processes we describe, f (t) = t c edges are added at each step. Thus the average degree k(t) ∝ t c .…”

Section: Introductionsupporting

confidence: 56%

“…The concept of accelerating growth was studied by Dorogovtsev and Mendes [12,13,14]. The papers distinguish between two types of power law degree distribution, stationary and non-stationary.…”

Section: Introductionmentioning

confidence: 99%

Scale‐free graphs of increasing degree

Cooper¹,

Prałat²

2011

Random Struct Algorithms

View full text Add to dashboard Cite

We study a scale-free random graph process in which the number of edges added at each step increases. This differs from the standard model in which a fixed number, m, of edges are added at each step.Let f (t) be the number of edges added at step t. In the standard scale-free model, f (t) = m constant, whereas in this paper we consider f (t) = [t c ], c > 0. Such a graph process, in which the number of edges grows non-linearly with the number of vertices is said to have accelerating growth.We analyze both an undirected and a directed process. The power law of the degree sequence of these processes exhibits widely differing behaviour.For the undirected process, the terminal vertex of each edge is chosen by preferential attachment based on vertex degree. When f (t) = m constant, this is the standard scalefree model, and the power law of the degree sequence is 3. When f (t) = [t c ], c < 1, the degree sequence of the process exhibits a power law with parameter x = (3 − c)/(1 − c). As c → 0, x → 3, which gives a value of x = 3, as in standard scale-free model. Thus no more slowly growing monotone function f (t) alters the power law of this model away from x = 3. When c = 1, so that f (t) = t, the expected degree of all vertices is t, the vertex degree is concentrated, and the degree sequence does not have a power law.For the directed process, the terminal vertex is chosen proportional to in-degree plus an additive constant, to allow the selection of vertices of in-degree zero. For this process when f (t) = m is constant, the power law of the degree sequence is x = 2 + 1/m. When f (t) = [t c ], c > 0, the power law becomes x = 1 + 1/(1 + c), which naturally extends the power law to (1,2].

show abstract

“…There is evidence to suggest that in the World Wide Web the average degree of a vertex is increasing with time, i.e., the parameter m appearing in the models is increasing. Dorogovtsev and Mendes [118,121] have studied a variation of the Barabási-Albert model that incorporates this process. They assume that the number m of new edges added per new vertex increases with network size n as n a for some constant a, and that the probability of attaching to a given vertex goes as k + Bn a for constant B.…”

Section: Generalizations Of the Barabási-albert Modelmentioning

confidence: 99%

The Structure and Function of Complex Networks

Newman¹

2003

View full text Add to dashboard Cite

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

show abstract

Accelerated growth of networks

Cited by 31 publications

References 50 publications

Densification arising from sampling fixed graphs

Densification arising from sampling fixed graphs

Scale‐free graphs of increasing degree

The Structure and Function of Complex Networks

Contact Info

Product

Resources

About