arXiv subjects

Mattia Marzi

Publications and source records attributed to Mattia Marzi.

5 recordsLinked to original sources

arXiv2026

Multiscale Reconstruction of Weighted Networks from Coarse-Grained Data

Network reconstruction from partial information is usually performed at the same resolution level at which constraints are observable. This becomes problematic when only coarse-grained information is available, while the relevant process occurs at a finer scale. Here we employ the multiscale model of weighted networks introduced in a companion paper and turn it into a probabilistic framework for reconstructing weighted networks across arbitrary aggregation levels. The model is built to preserve its functional form under coarse-graining, so that global parameters calibrated on an observable aggregate layer can be transferred to finer layers without refitting. We test the method on two empirical systems with different aggregation mechanisms. In the International Trade Network, countries are aggregated into geographic macro-regions and the observed coarse-grained layer is used to infer the underlying country-level network. In the Dutch production network, sectoral flows are reconstructed across the hierarchical industrial classification, using coarser sectoral layers to infer finer ones. In both geographical and sectoral settings, we benchmark our genuinely multiscale reconstruction method against a state-of-the-art weighted reconstruction model calibrated directly at the target resolution, and therefore using additional information available at the same (finer) scale at which performance is evaluated. Remarkably, despite this informational disadvantage, our method recovers the fine-scale binary structure with high accuracy, improving precision, specificity, accuracy and maximum degree-error diagnostics, while remaining nearly equivalent in sensitivity.

physics.soc-ph↗

arXiv2026

Multiscale Renormalization of Weighted Networks

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.

physics.soc-ph↗

arXiv2026

The hidden structure of innovation networks

Innovation emerges from complex collaboration patterns - among inventors, firms, or institutions. However, not much is known about the overall mesoscopic structure around which inventive activity self-organizes. Here, we tackle this problem by employing patent data to analyze both individual (\textit{co-inventorship}) and organization (\textit{co-ownership}) networks in three strategic domains (\textit{artificial intelligence}, \textit{biotechnology} and \textit{semiconductors}). We characterize the mesoscale structure (in terms of clusters) of each domain by comparing two alternative methods: a standard baseline - modularity maximization - and one based on the minimization of the Bayesian Information Criterion, within the Stochastic Block Model and its degree-corrected variant. We find that, across sectors, inventor networks are denser and more clustered than organization ones - consistently with the presence of small recurrent teams embedded into broader institutional hierarchies - whereas organization networks have a neater role-based structures, with few bridging firms coordinating the most peripheral ones; still, both are characterized by the presence of local core-periphery structures. We also find that the discovered meso-structures are connected to innovation output. In particular, Lorenz curves of forward citations show a pervasive inequality in technological influence: across sectors and methods, both inventor (especially) and organization networks consistently show high levels of concentration of citations in a few of the discovered clusters. Our results demonstrate that the baseline modularity-based method may not be capable of fully capturing the way collaborations drive the spreading of inventive impact across technological domains. This is due to the presence of local hierarchies that call for the more refined tools of Bayesian inference.

econ.GN↗

arXiv2026

A Bayesian approach to out-of-sample network reconstruction

Networks underpin systems that range from finance to biology, yet their structure is often only partially observed. Current reconstruction methods typically fit the parameters of a model anew to each snapshot, thus offering no guidance to predict future configurations. Here, we develop a Bayesian approach that uses the information about past network snapshots to inform a prior and predict the subsequent ones, while quantifying uncertainty. Instantiated with a single-parameter fitness model, our method infers link probabilities from node strengths and carries information forward in time. When applied to the Electronic Market for Interbank Deposit across the years 1999-2012, our method accurately recovers the number of connections per bank at subsequent times, outperforming probabilistic benchmarks designed for analogous, link prediction tasks. Notably, each predicted snapshot serves as a reliable prior for the next one, thus enabling self-sustained, out-of-sample reconstruction of evolving networks with a minimal amount of additional data.

physics.soc-ph↗

arXiv2026

Reproducing the first and second moments of empirical degree distributions

The study of probabilistic models for the analysis of complex networks represents a flourishing research field. Among the former, Exponential Random Graphs (ERGs) have gained increasing attention over the years. So far, only linear ERGs have been extensively employed to gain insight into the structural organisation of real-world complex networks. None, however, is capable of accounting for the variance of the empirical degree distribution. To this aim, non-linear ERGs must be considered. After showing that the usual mean-field approximation forces the degree-corrected version of the two-star model to degenerate, we define a fitness-induced variant of it. Such a `softened' model is capable of reproducing the sample variance, while retaining the explanatory power of its linear counterpart, within a purely canonical framework.

physics.soc-ph↗