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Spawning Nodes Generate Deterministic Scale-Free Networks

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Peter R. Conwell, Kaushik Chakram, Valeria J. Villegas-Medina

Social and Information Networks · Submitted 26 May 2023

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

The authors' main claim We show theoretically and with simulations that such a spawned network will have a degree distribution obeying a power law with exponent 2.5.

how it is stated · asserted 1.00 read the record →

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arXiv ID2305.16980 (version 1)
Pith IDYVFF46EJ, Pith's permanent record of this paper and its review
CitationKaushik Chakram, Peter R. Conwell, Valeria J. Villegas-Medina. "Spawning Nodes Generate Deterministic Scale-Free Networks." arXiv:2305.16980 (2023). https://pith.science/paper/YVFF46EJ
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,394 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.44 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.02 · states quantitative result 0.98 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we present a deterministic vertex spawning model that yields a scale-free network. The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and inversely proportional to the number of edges currently connected to the parent. Spawned offspring maintain an undirected edge with its parent. No information about the network as a whole is required to obtain scale-invariant behavior. Although the algorithm is deterministic, the number of nodes spawning in a small time interval quickly becomes randomized. We show theoretically and with simulations that such a spawned network will have a degree distribution obeying a power law with exponent 2.5. Simulations show that the distribution matches a Zipf distribution.

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 In this paper we present a deterministic vertex spawning model that yields a scale-free network. contribution 1.00 0.92 0.76 asserted 1.00
s1 The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and inversely proportional to the number of edges currently connected to the parent. method 1.00 0.62 0.06 asserted 0.98
s2 Spawned offspring maintain an undirected edge with its parent. method 1.00 0.41 0.03 asserted 1.00
s3 No information about the network as a whole is required to obtain scale-invariant behavior. interpretation 0.46 0.55 0.09 asserted 1.00
s4 Although the algorithm is deterministic, the number of nodes spawning in a small time interval quickly becomes randomized. result 0.68 0.80 0.04 asserted 0.98
s5 We show theoretically and with simulations that such a spawned network will have a degree distribution obeying a power law with exponent 2.5. result 0.99 0.95 0.74 asserted 1.00
s6 Simulations show that the distribution matches a Zipf distribution. result 0.97 0.91 0.11 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.60 · evidence from simulation or computation 0.73.

What was examined, and what was not

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  • 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

In this paper we present a deterministic vertex spawning model that yields a scale-free network. The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and inversely proportional to the number of edges currently connected to the parent. Spawned offspring maintain an undirected edge with its parent. No information about the network as a whole is required to obtain scale-invariant behavior. Although the algorithm is deterministic, the number of nodes spawning in a small time interval quickly becomes randomized. We show theoretically and with simulations that such a spawned network will have a degree distribution obeying a power law with exponent 2.5. Simulations show that the distribution matches a Zipf distribution.

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What this paper does with the arXiv papers it cites

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

What it cites

Uses the method or tool of 1 paper
  • Assuming the results indicated we had degree distribution with a power law of the form Eq.([ref]), we attempted the methods discussed in [ref] to identify the value of $α$.

    Power-law distributions in empirical data · Results · 1.00

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