Emergence of Scaling in Random Networks.¶
Barabási, A., & Albert, R. (1999). Emergence of Scaling in Random Networks. Science, 286(5439), 509-512.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Complexity
- Network science (Albert-Barabási on scale-free networks, Newman on network structure) showed that topology alone—the pattern of connections—generates emergent behavior (cascading failures, epidemic spread, synchronization) independent of individual node properties
This sourceScale-free network topology arises from growth + preferential attachment; network structure alone generates emergent behavior across systems. Re-sourced replacement for D26-079: the marker sits on the network-science sentence (Albert-Barabási scale-free networks, Newman) about topology generating cascading failures/synchronization, but the original key (holland-1995, Hidden Order, a complex-adaptive-systems book) does not cover network topology and does not support that specific sentence.
- Network science (Albert-Barabási on scale-free networks, Newman on network structure) showed that topology alone—the pattern of connections—generates emergent behavior (cascading failures, epidemic spread, synchronization) independent of individual node properties
- Heavy-Tailed Distributions
- Network science: Degree distributions of many real networks are approximately scale-free, so a few hub nodes carry most of the connectivity, define the network's robustness to random failure, and simultaneously make it fragile to targeted attack on the hubs.
This sourcePreferential-attachment model for scale-free networks. Concurrent empirical discovery of Internet power-law degrees: Faloutsos, Faloutsos, and Faloutsos, SIGCOMM 1999. Monograph: Barabási, Network Science (Cambridge UP, 2016).
- Network science: Degree distributions of many real networks are approximately scale-free, so a few hub nodes carry most of the connectivity, define the network's robustness to random failure, and simultaneously make it fragile to targeted attack on the hubs.
- Network
- … Erdős and Rényi's 1959 random-graph model (the first rigorous probabilistic theory of large graphs), was transformed by Milgram's 1967 small-world experiment, Watts and Strogatz's 1998 small-world network model (reconciling high clustering with short path lengths), Barabási and Albert's 1999 scale-free network model
This sourcePreferential-attachment model for scale-free networks. Concurrent empirical discovery of Internet power-law degrees: Faloutsos, Faloutsos, and Faloutsos, SIGCOMM 1999. Monograph: Barabási, Network Science (Cambridge UP, 2016).
- … Erdős and Rényi's 1959 random-graph model (the first rigorous probabilistic theory of large graphs), was transformed by Milgram's 1967 small-world experiment, Watts and Strogatz's 1998 small-world network model (reconciling high clustering with short path lengths), Barabási and Albert's 1999 scale-free network model
- Propagation
- The reasoning is structural, not content-specific—a generality Barabási and Albert (1999) ground by showing that scale-free topology emerges as a common organizing principle across radically different network substrates.
This sourcePreferential-attachment model for scale-free networks. Concurrent empirical discovery of Internet power-law degrees: Faloutsos, Faloutsos, and Faloutsos, SIGCOMM 1999. Monograph: Barabási, Network Science (Cambridge UP, 2016).
- The reasoning is structural, not content-specific—a generality Barabási and Albert (1999) ground by showing that scale-free topology emerges as a common organizing principle across radically different network substrates.
- Scale Invariance
- Complex networks (social networks, protein interactions, the World Wide Web) exhibit power-law degree distributions, P(k) ∝ k^(−γ) with γ typically 2–3
This sourcePreferential-attachment mechanism generating scale-free networks with power-law degree distributions.
- Complex networks (social networks, protein interactions, the World Wide Web) exhibit power-law degree distributions, P(k) ∝ k^(−γ) with γ typically 2–3
- Single Point of Failure
- The abstraction also licenses comparison across substrates: a keystone species and a master database are the same object under different names, both articulation nodes whose removal disconnects the graph they sit in.
This sourceFoundational scale-free-network result; underpins the cross-substrate identity of hub/articulation nodes whose removal fragments otherwise-broad networks.
- The abstraction also licenses comparison across substrates: a keystone species and a master database are the same object under different names, both articulation nodes whose removal disconnects the graph they sit in.
- Universality
- Linguistics: structural universals (recursion, constituent-ordering correlations, recurring phonological attractors) recur across historically unrelated languages, predictable from a small set of cognitive constraints rather than any language's particular history. Network science: scale-free degree distributions emerge in citation graphs, the web, protein-interaction networks, and food webs despite different growth mechanisms.
This sourceShows scale-free degree distributions emerge across citation, web, and biological networks via preferential attachment regardless of micro growth detail.
- Linguistics: structural universals (recursion, constituent-ordering correlations, recurring phonological attractors) recur across historically unrelated languages, predictable from a small set of cognitive constraints rather than any language's particular history. Network science: scale-free degree distributions emerge in citation graphs, the web, protein-interaction networks, and food webs despite different growth mechanisms.
Verification¶
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