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.
Supported in partVerified against the work's full text
Barabasi and Albert show a scale-free degree distribution arising from growth and preferential attachment regardless of system or constituent identity; they do not treat cascades, epidemics or synchronization.
“independent of the system and the ide ntity of its constituents”
- 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).
Supported in partVerified against the work's full text
Supports that many real networks have scale-free power-law degree distributions with hubs; says nothing on robustness to random failure or fragility to targeted attack.
“A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution.”
- 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).
SupportedVerified against the work's full text
Barabasi and Albert report power-law degree distributions across WWW, citation and actor networks independent of the system, attributing them to generic growth and preferential attachment.
“in science we show that, independent of the system and the ide ntity of its constituents, the probability P (k) that a vertex in the network interacts with k other vertices decays as a power-law”
- 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.
Supported in partVerified against the work's full text
Barabasi and Albert report power-law degree distributions for actor collaboration (gamma 2.3) and WWW (2.1) networks, but give no protein-interaction data and a range of 2.1 to 4.
“power-law for large k, with an exponent γ between 2.1 and 4”
- 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.
Supported in partVerified against the work's full text
Shows hub vertices recur across very different networks (web, power grid, actors, citations), but says nothing about keystone species, databases or what removing a node does.
“highly connected (large k) vertices have a large chance of occurring”
- 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.
Supported in partVerified against the work's full text
Shows power-law degree distributions in the actor network, web, power grid and citation data, driven by growth and preferential attachment; protein and food-web networks are not examined.
“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.”
- 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¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 6 of 7 citations: 1 supported, 5 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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