Pseudofractal scale-free web.

By Sergey N. Dorogovtsev, A. Goltsev, José Fernando Ferreira Mendes. Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

494 citations recorded by the source corpus.

We find that scale-free random networks are excellently modeled by simple deterministic graphs. Our graph has a discrete degree distribution (degree is the number of connections of a vertex), which is characterized by a power law with exponent gamma=1+ln 3/ln 2. Properties of this compact structure are surprisingly close to those of growing random scale-free networks with gamma in the most interesting region, between 2 and 3. We succeed to find exactly and numerically with high precision all main characteristics of the graph. In particular, we obtain the exact shortest-path-length distribution. For a large network (ln N>>1) the distribution tends to a Gaussian of width approximately sqrt[ln N] centered at (-)l approximately ln N. We show that the eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail with exponent 2+gamma.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f36564c2e96dcdc4513dde960016a7f69da2d5a5

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In Condensed Matter Physics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Distances in Random Graphs with Finite Mean and Infinite Variance Degrees (2005, background): “[17, 18] investigate the leading asymptotics and the fluctuations around the mean of the graph distance between arbitrary nodes from a theoretical physics point of view, using mainly generating functions.”
Kronecker Graphs: An Approach to Modeling Networks (2008, methodology): “Moreover, especially web graphs (Dill et al., 2002; Dorogovtsev et al., 2002; Crovella and Bestavros, 1997) and biological networks (Ravasz and Barabási, 2003) were found to be self-similar and “fractal”.”
Evolution and Structure of the Internet: Index (2004, background): “At the same time, the use of hierarchical constructions in growing network models is still at an early stage (Dorogovtsev et al., 2002; Jung et al., 2002; Ravasz and Barabási, 2003).”
Random walks and diffusion on networks (2016, background): “iety of pseudo-fractals by exploiting the recursive nature of their denitions. Before general (u;v)- owers were proposed in Ref. [165], the special case with u = 1 and v = 2 had already been studied [162]. A (1;2)- ower has degree distribution p(k) /k , where = 1 + ln3=ln2 ˇ2:59 [162]. A (u;v)- ower”
Similarities and Differences in Genome-Wide Expression Data of Six Organisms (2003, background): “However, deterministic models that lead to a hierarchical organization of modularity predict C ; k (Dorogovtsev et al. 2002; Ravasz and Barabasi 2003).”
Critical phenomena in complex networks (2007, methodology): “For detailed discussion of these problems, see, e.g., Dorogovtsev et al. (2002a), Dorogovtsev (2003), and Rozenfeld and ben-Avraham (2007).”
Synchronization in complex networks (2008, background): “Additionally, the authors studied two types of deterministic SF networks: a pseudofractal SF network introduced by Dorogovtsev et al. (2002) and the Apollonian network introduced by Andrade et al. (2005).”
The Structure and Function of Complex Networks (2003, methodology): “Dorogovtsev and Mendes [122] have expanded their above-mentioned review into a book, which again focuses on models of growing graphs.”
Network biology: understanding the cell's functional organization (2004, background): “The quantifiable signature of hierarchical modularity is the dependence of the clustering coefficient on the degree of a node, which follows C ( k ) ∼ k −1 (Ref”
Origins of fractality in the growth of complex networks (2005, methodology): “We show that the key principle that gives rise to the fractal architecture of networks is a strong effective “repulsion” (disassortativity) between the most connected nodes (hubs) on all length scales, rendering them very dispersed.”
Indicators for Complex Innovation Systems (2006, background): “These laws typify many characteristics of innovation systems (De Solla Price, 1963).”