Multiscale Renormalization of Weighted Networks
Abstract
Recent progress in network renormalization has identified various ways to transform network representations consistently across resolution levels. In particular, the renormalization flow describing how random graph models transform under node aggregation has identified a fixed point corresponding to an aggregation-invariant model that preserves the form of the connection probability across arbitrary scales. While this probabilistic multiscale approach has successfully been used to model real-world networks, construct latent-space node embeddings, and reconstruct finer-grained versions of aggregate network data in a principled resolution-invariant way, it has so far been restricted to binary graphs. Here we reformulate multiscale network renormalization for weighted random graphs. Via a generating-function approach, we identify a weighted multiscale model whose full probability law, encoding both link creation and weight assignment, has an invariant compound-Poisson form under arbitrary node aggregation. The renormalization rules that transform parameters across aggregation levels allow the ensemble to be calibrated at one level and applied at another, enabling consistent modeling and reconstruction of weighted networks across arbitrary scales.
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BibTeX
@misc{marzi2026multiscale,
title = {{Multiscale Renormalization of Weighted Networks}},
author = {Mattia Marzi and Frank P. Pijpers and Diego Garlaschelli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38283},
eprint = {2609.38283},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38283},
}
RIS
TY - UNPB
TI - Multiscale Renormalization of Weighted Networks
AU - Mattia Marzi
AU - Frank P. Pijpers
AU - Diego Garlaschelli
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38283
UR - https://arxiv.org/abs/2609.38283
AB - Recent progress in network renormalization has identified various ways to transform network representations consistently across resolution levels. In particular, the renormalization flow describing how random graph models transform under node aggregation has identified a fixed point corresponding to an aggregation-invariant model that preserves the form of the connection probability across arbitrary scales. While this probabilistic multiscale approach has successfully been used to model real-world networks, construct latent-space node embeddings, and reconstruct finer-grained versions of aggregate network data in a principled resolution-invariant way, it has so far been restricted to binary graphs. Here we reformulate multiscale network renormalization for weighted random graphs. Via a generating-function approach, we identify a weighted multiscale model whose full probability law, encoding both link creation and weight assignment, has an invariant compound-Poisson form under arbitrary node aggregation. The renormalization rules that transform parameters across aggregation levels allow the ensemble to be calibrated at one level and applied at another, enabling consistent modeling and reconstruction of weighted networks across arbitrary scales.
ER -