arXiv subjects

Helcio Felippe

Publications and source records attributed to Helcio Felippe.

4 recordsLinked to original sources

arXiv2026

Hypergraph backboning

Hypergraphs provide a natural framework for describing complex networked systems with higher-order, non-dyadic interactions. Due to their high dimensionality and often redundant structure, a key challenge is to develop methods that simplify hypergraph representations while preserving the essential structure of interactions. Here we present a principled, efficient, and non-parametric information-theoretic method for pruning nested and/or redundant structures in hypergraphs, enabling a minimal representation of higher-order interactions in the presence of local heterogeneity. Our approach naturally extends to weighted hypergraphs, where higher-order topology and hyperedge weights combine to identify the system's structural backbone. We validate the method on controlled synthetic hypergraphs and apply it to empirical datasets from diverse domains, demonstrating substantial sparsification without loss of core structural information.

cs.SI↗

arXiv2026

Structural reducibility of hypergraphs

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater computational demands than their pairwise counterparts. Here we present an information-theoretic framework for determining the extent to which a hypergraph representation of a networked system is structurally redundant, and for identifying its most critical higher orders of interaction that allow us to remove these redundancies while preserving essential higher-order structure.

physics.soc-ph↗

arXiv2025

Information theory for hypergraph similarity

Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network comparison are limited to pairwise interactions only. Here we construct a general information theoretic framework for hypergraph similarity, capturing meaningful correspondence among higher-order interactions while correcting for spurious correlations. Our method operationalizes any notion of structural overlap among hypergraphs as a principled normalized mutual information measure, allowing us to derive a hierarchy of increasingly granular formulations of similarity among hypergraphs within and across orders of interactions, and at multiple scales. We validate these measures through extensive experiments on synthetic hypergraphs and apply the framework to reveal meaningful patterns in a variety of empirical higher-order networks. Our work provides foundational tools for the principled comparison of higher-order networks, shedding light on the structural organization of networked systems with non-dyadic interactions.

physics.soc-ph↗

arXiv2024

Network mutual information measures for graph similarity

A wide range of tasks in network analysis, such as clustering network populations or identifying anomalies in temporal graph streams, require a measure of the similarity between two graphs. To provide a meaningful data summary for downstream scientific analyses, the graph similarity measures used for these tasks must be principled, interpretable, and capable of distinguishing meaningful overlapping network structure from statistical noise at different scales of interest. Here we derive a family of graph mutual information measures that satisfy these criteria and are constructed using only fundamental information theoretic principles. Our measures capture the information shared among networks according to different encodings of their structural information, with our mesoscale mutual information measure allowing for network comparison under any specified network coarse-graining. We test our measures in a range of applications on real and synthetic network data, finding that they effectively highlight intuitive aspects of network similarity across scales in a variety of systems.

physics.soc-ph↗