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Lyapunov Exponents for Temporal Networks

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Annalisa Caligiuri, Victor M. Eguiluz, Leonardo di Gaetano, Tobias Galla, Lucas Lacasa

Data Analysis, Statistics and Probability · Submitted 30 Jan 2023

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

The authors' main claim We validate our method for a range of synthetic generative network models displaying low and high dimensional chaos, and finally discuss potential applications.

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arXiv ID2301.12966 (version 1)
Pith IDIA5B3JLR, Pith's permanent record of this paper and its review
CitationAnnalisa Caligiuri, Leonardo Di Gaetano, Lucas Lacasa, Tobias Galla, Victor M. Eguiluz. "Lyapunov Exponents for Temporal Networks." arXiv:2301.12966 (2023). https://pith.science/paper/IA5B3JLR
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,016 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions, and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low and high dimensional chaos, and finally discuss potential applications.

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 By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE) of a temporal network trajectory. contribution 0.99 0.95 0.34 asserted 1.00
s1 Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions, and estimate the nMLE directly from a single network trajectory. method 0.83 0.93 0.21 asserted 1.00
s2 We validate our method for a range of synthetic generative network models displaying low and high dimensional chaos, and finally discuss potential applications. result 0.32 0.94 0.17 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.99.

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  • 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

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions, and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low and high dimensional chaos, and finally discuss potential applications.

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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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