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A Note on the Modeling Power of Different Graph Types

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Josephine M. Thomas, Silvia Beddar-Wiesing, Alice Moallemy-Oureh, Rüdiger Nather

Discrete Mathematics · Submitted 22 Sep 2021

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

The authors' main claim Additionally, we show that all attributed graph types are equally expressive and have the same modeling power.

how it is stated · asserted 1.00 read the record →

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arXiv ID2109.10708 (version 2)
Pith IDNXSC2GEN, Pith's permanent record of this paper and its review
CitationAlice Moallemy-Oureh, Josephine M. Thomas, R\"udiger Nather, Silvia Beddar-Wiesing. "A Note on the Modeling Power of Different Graph Types." arXiv:2109.10708 (2021). https://pith.science/paper/NXSC2GEN
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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, 3,502 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph types based on an expressivity relation. The expressivity relation quantifies how many properties a graph type can encode compared to another type. Additionally, we show that all attributed graph types are equally expressive and have the same modeling power.

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 Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. background 1.00 0.06 0.04 hedged possibility 0.95
s1 In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph types based on an expressivity relation. contribution 0.95 0.94 0.10 asserted 0.94
s2 The expressivity relation quantifies how many properties a graph type can encode compared to another type. method 0.83 0.44 0.07 asserted 1.00
s3 Additionally, we show that all attributed graph types are equally expressive and have the same modeling power. result 1.00 0.94 0.55 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.95.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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

Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph types based on an expressivity relation. The expressivity relation quantifies how many properties a graph type can encode compared to another type. Additionally, we show that all attributed graph types are equally expressive and have the same modeling power.

Human review

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How the literature uses it

2 arXiv papers cite this in 8 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

Papers citing it · 7 sentences without a confident label

Cites it as background 1 paper

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