Emergence of scaling in random networks

By Albert-László Barabási, Réka Albert. 1999

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

Subfields: Scaling & Learning Theory

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Citations in the corpus

Gradient-Based Neural DAG Learning (2019, methodology): “Scale-free (SF) graphs were generated using the Barab´asi-Albert model (Barab´asi & Albert, 1999) which is based on preferential attachment.”
Scalable training of artificial neural networks with adaptive sparse connectivity inspired by network science (2017, neutral): “6 and include scale-freeness 7 (detailed in Methods section) and small-worldness 8 .”
DAGs with NO TEARS: Continuous Optimization for Structure Learning (2018, methodology): “Since real-world networks often exhibit scale-free and small-world topologies (Watts and Strogatz, 1998; Barabási and Albert, 1999) with highly connected hub nodes, these kinds of structural assumptions are not only difficult to satisfy, but impossible to check.”
Graph evolution: Densification and shrinking diameters (2006, background): “wing diameter assumption: The diameter is a slowly growing function of the network size, as in “small world” graphs [6, 11, 38, 50]. For example, the intensively-studied preferential attachment model [5, 40] posits a network in which each new node, when it arrives, attaches to the existing network b”
The protein folding network. (2004, background): “The power-law is due to the presence of a few largely connected “hubs” while the majority of the nodes have a relatively small number of links.(35) This behavior has been previously observed for several biological,(8) social(36) and technological networks,(9) which in the literature take the name of”
A model of Internet topology using k-shell decomposition (2006, background): “idea to ”scale-free” graphs, with a long-tailed power law distribution of node degree, is a natural one. See [12] for a detailed discussion of the statistics of the k-cores in preferential attachment [13] graphs of 106 nodes and various degree distribution power laws, and for heuristic arguments lin”
Structure and Dynamics of Networks (2009, background): “One of the most obvious and prominent examples is the Internet [Albert et al., 1999, Barabási & Albert, 1999, Pastor-Satorras & Vespignani, 2004].”
A time-varying complex dynamical network model and its controlled synchronization criteria (2004, unknown): “e is a fundamental unit, which can have diﬀerent meanings in diﬀerent situations, such as chemical substrates, microprocessors or computers, schools or companies, papers, webs, even people, and so on [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. Examples of complex networks in”
Agent-based simulation of innovation diffusion: a review (2011, background): “A network model that captures this characteristic was proposed by Barabási and Albert (1999).”
Counting triangles and the curse of the last reducer (2011, background): “salient feature of massive social network data is that there are typically several nodes with extraordinarily high degree [1].”