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On the structural properties of small-world networks with finite range of shortcut links

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Tao Jia, Rahul V. Kulkarni

Physics and Society · Submitted 28 Feb 2011

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

The authors' main claim We observe the small-world phenomenon for $r \ll 1$ indicating that global shortcuts are not necessary for the small-world effect.

how it is stated · hedged possibility 0.63 read the record →

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arXiv ID1103.0048 (version 1)
Pith ID7HMZNCYF, Pith's permanent record of this paper and its review
CitationRahul V. Kulkarni, Tao Jia. "On the structural properties of small-world networks with finite range of shortcut links." arXiv:1103.0048 (2011). https://pith.science/paper/7HMZNCYF
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The compiled record

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, 4,877 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.59 · randomized assignment 0.01 · states quantitative result 0.33 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the original SWN model. These short-range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenomenon for $r \ll 1$ indicating that global shortcuts are not necessary for the small-world effect. For short-range SWNs, the average path length changes nonmonotonically with system size, whereas for the original SWN model it increases monotonically. We propose an expression for the average path length for short-range SWNs based on numerical simulations and analytical approximations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. contribution 0.99 0.88 0.07 asserted 0.97
s1 When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the original SWN model. method 0.64 0.32 0.06 asserted 1.00
s2 These short-range SWNs have a similar degree distribution and scaling properties as the original SWN model. result 1.00 0.77 0.15 asserted 1.00
s3 We observe the small-world phenomenon for $r \ll 1$ indicating that global shortcuts are not necessary for the small-world effect. interpretation 0.75 0.91 0.47 hedged possibility 0.63
s4 For short-range SWNs, the average path length changes nonmonotonically with system size, whereas for the original SWN model it increases monotonically. result 1.00 0.92 0.23 asserted 1.00
s5 We propose an expression for the average path length for short-range SWNs based on numerical simulations and analytical approximations. contribution 0.89 0.95 0.14 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.56 · evidence from simulation or computation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • 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

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the original SWN model. These short-range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenomenon for $r \ll 1$ indicating that global shortcuts are not necessary for the small-world effect. For short-range SWNs, the average path length changes nonmonotonically with system size, whereas for the original SWN model it increases monotonically. We propose an expression for the average path length for short-range SWNs based on numerical simulations and analytical approximations.

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