Hypergraphx: a library for higher-order network analysis (2303.15356v1)

Abstract: From social to biological systems, many real-world systems are characterized by higher-order, non-dyadic interactions. Such systems are conveniently described by hypergraphs, where hyperedges encode interactions among an arbitrary number of units. Here, we present an open-source python library, hypergraphx (HGX), providing a comprehensive collection of algorithms and functions for the analysis of higher-order networks. These include different ways to convert data across distinct higher-order representations, a large variety of measures of higher-order organization at the local and the mesoscale, statistical filters to sparsify higher-order data, a wide array of static and dynamic generative models, and an implementation of different dynamical processes with higher-order interactions. Our computational framework is general, and allows to analyse hypergraphs with weighted, directed, signed, temporal and multiplex group interactions. We provide visual insights on higher-order data through a variety of different visualization tools. We accompany our code with an extended higher-order data repository, and demonstrate the ability of HGX to analyse real-world systems through a systematic analysis of a social network with higher-order interactions. The library is conceived as an evolving, community-based effort, which will further extend its functionalities over the years. Our software is available at https://github.com/HGX-Team/hypergraphx

• The paper introduces HGX, a library that advances higher-order network analysis through flexible representations like bipartite and line graph transformations.
• The paper details comprehensive statistical and community detection tools, including spectral centrality and motif analysis, to evaluate complex hypergraph structures.
• The paper demonstrates HGX’s capability to simulate and visualize dynamical processes, enhancing studies of non-dyadic interactions in diverse scientific fields.

Hypergraphx: A Comprehensive Library for Higher-Order Network Analysis

The paper "Hypergraphx: a library for higher-order network analysis" discusses the development and functionalities of hypergraphx (HGX), an advanced open-source Python library aimed at facilitating comprehensive analysis of higher-order networks defined by hypergraphs. Such networks are fundamentally different from traditional dyadic networks, as they encapsulate interactions among multiple units (nodes) simultaneously, making them particularly suitable for analyzing complex systems with non-dyadic interactions prevalent in biological, technological, and social settings.

Key Features and Functionalities

HGX presents a robust computational infrastructure that accommodates diverse features characteristic of higher-order networks, such as weighted, directed, signed, temporal, and multiplex group interactions. The library is designed to be highly flexible, supporting a broad range of analytical methodologies:

• Representational Flexibility: Users can transform hypergraphs into alternate representations like bipartite networks or higher-order line graphs, facilitating analyses tailored to specific research inquiries.
• Centrality and Statistics: HGX provides a plethora of statistical tools for evaluating node and hyperedge properties, including hyperdegree distributions and assortativity measures. Multiple centrality measures are designed to assess node importance in varying interaction group sizes, employing methods such as spectral approaches.
• Community and Motif Analysis: The library includes sophisticated community detection algorithms suitable for hypergraphs, such as spectral methods and models that extract overlapping communities. It also empowers motif analysis, which is pivotal for identifying recurring subgraph patterns indicative of functional and structural network building blocks.
• Generative Models: To support theoretical explorations and algorithms benchmarking, HGX offers implementations for generating synthetic hypergraphs with specified topological features, including Erdős–Rényi and scale-free models, facilitating the examination of mesoscale organization.
• Dynamical Processes Simulation: The library encompasses tools to simulate and analyze the impacts of higher-order interactions on dynamical processes like synchronization and contagion, leveraging frameworks such as the Master Stability Function and perspectives on simplicial contagion.
• Visualization and Data: Recognizing the importance of visual insights, HGX includes diverse visualization tools to graphically represent higher-order interactions. The library is supplemented with a higher-order data repository, enabling users to explore and test methodologies on curated datasets across various scientific domains.

Implications and Future Directions

The introduction of HGX fills a crucial gap in computational methodologies for network science, enabling researchers to harness the complexity of higher-order interactions with efficiency and accuracy. While the library provides a comprehensive toolkit, its design as a community-driven project invites extensions and enhancements, ensuring it remains a cutting-edge resource as the field evolves. Prospective developments could encompass methods to assess network robustness, dimensionality reduction techniques, and expanded dynamical models, including ecological dynamics or information-theoretic measures.

In conclusion, HGX not only democratizes access to sophisticated higher-order network analysis tools but also sets a platform for continued advancements in understanding complex systems. By enhancing our ability to model and analyze non-dyadic interactions, the library has the potential to significantly impact diverse research areas spanning social sciences, biology, and beyond. Researchers are encouraged to engage with this resource, contributing to its evolution and applying it to explore the nuanced dynamics of higher-order networks.