The evolution of navigable small-world networks

Ian Clarke; Oskar Sandberg

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The evolution of navigable small-world networks

Oskar Sandberg, Ian Clarke

Data Structures and Algorithms · Submitted 7 Jul 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The resulting process gives a model for the evolution of small-world networks with properties similar to those studied by Kleinberg.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,203 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.09 · human participants 0.03 · controlled comparison 0.09 · randomized assignment 0.03 · states quantitative result 0.04 · compares with prior results 0.87 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Small-world networks, which combine randomized and structured elements, are seen as prevalent in nature. Several random graph models have been given for small-world networks, with one of the most fruitful, introduced by Jon Kleinberg, showing in which type of graphs it is possible to route, or navigate, between vertices with very little knowledge of the graph itself. Kleinberg's model is static, with random edges added to a fixed grid. In this paper we introduce, analyze and test a randomized algorithm which successively rewires a graph with every application. The resulting process gives a model for the evolution of small-world networks with properties similar to those studied by Kleinberg.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Small-world networks, which combine randomized and structured elements, are seen as prevalent in nature.	background 1.00	0.03	0.03	asserted 0.95
s1	Several random graph models have been given for small-world networks, with one of the most fruitful, introduced by Jon Kleinberg, showing in which type of graphs it is possible to route, or navigate, between vertices with very little knowledge of the graph itself.	background 1.00	0.04	0.05	asserted 0.98
s2	Kleinberg's model is static, with random edges added to a fixed grid.	background 0.96	0.04	0.03	asserted 1.00
s3	In this paper we introduce, analyze and test a randomized algorithm which successively rewires a graph with every application.	contribution 0.71	0.94	0.12	asserted 0.99
s4	The resulting process gives a model for the evolution of small-world networks with properties similar to those studied by Kleinberg.	result 0.49	0.79	0.51	asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.80 · evidence from simulation or computation 0.59.

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arXiv listing abstract v1

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full text
figures and tables
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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Small-world networks, which combine randomized and structured elements, are seen as prevalent in nature. Several random graph models have been given for small-world networks, with one of the most fruitful, introduced by Jon Kleinberg, showing in which type of graphs it is possible to route, or navigate, between vertices with very little knowledge of the graph itself. Kleinberg's model is static, with random edges added to a fixed grid. In this paper we introduce, analyze and test a randomized algorithm which successively rewires a graph with every application. The resulting process gives a model for the evolution of small-world networks with properties similar to those studied by Kleinberg.

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2 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 2 papers

Sandberg and Clarke [ref] propose another rewiring dynamic where with an independent probability of $p$ each node on a greedy search path would rewire their long-range contacts to the search target, and provide a partial analysis and simulations showing that the dynamic converges to a network close to the navigable small world.

A Game Theoretic Model for the Formation of Navigable Small-World Networks --- the Tradeoff between Distance and Reciprocity · Introduction · 0.87
[ref] conjecture that when the chain achieves stationarity, the distribution of distances spanned by long-range links is (close to) theoretical optimum for search and the expected length of searches is polylogarithmic.

A survey of statistical network models · Small-World Models · 0.84

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