Graphlets in multilayer networks

Physical and functional constraints on biological networks lead to complex topological patterns across multiple scales in their organization. A particular type of higher-order network feature that has received considerable interest is network motifs, defined as statistically regular subgraphs. These may implement fundamental logical and computational circuits and are referred to as “building blocks of complex networks”. Their well-defined structures and small sizes also enable the testing of their functions in synthetic and natural biological experiments. Here, we develop a framework for motif mining based on lossless network compression using subgraph contractions. This provides an alternative definition of motif significance which allows us to compare different motifs and select the collectively most significant set of motifs as well as other prominent network features in terms of their combined compression of the network. Our approach inherently accounts for multiple testing and correlations between subgraphs and does not rely on a priori specification of an appropriate null model. It thus overcomes common problems in hypothesis testing-based motif analysis and guarantees robust statistical inference. We validate our methodology on numerical data and then apply it on synaptic-resolution biological neural networks, as a medium for comparative connectomics, by evaluating their respective compressibility and characterize their inferred circuit motifs.

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pymnet: A Python Library for Multilayer Networks

Nurmi,

Badie-Modiri,

Coupette

et al. 2024

JOSS

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Many complex systems can be readily modeled as networks and represented as graphs. Such systems include social interactions, transport infrastructures, biological pathways, brains, ecosystems, and many more. A major advantage of representing complex systems as graphs is that the same graph tools and methods can be applied in a wide variety of domains. However, the graph representation has its limitations: many systems contain nodes with multidimensional features, interactions of various types, different levels of hierarchy, or multiple modalities, which deserve to be modeled but cannot be described by simple graphs. Multilayer networks (Kivelä et al., 2014) generalize graphs to capture the rich network data often associated with complex systems, allowing us to study a broad range of phenomena using the same representations, tools, and methods. With pymnet, we introduce a Python package that provides the essential data structures and computational tools for multilayer-network analysis. As highlights, the library offers efficient and scalable implementations for sparse multilayer networks and multiplex networks, integration with bliss to analyze multilayernetwork isomorphisms and automorphisms, and versatile methods for multilayer-network visualization.

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Graphlets in multilayer networks

Cited by 3 publications

References 48 publications

Towards the Concept of Spatial Network Motifs

Towards the Concept of Spatial Network Motifs

Compression-based inference of network motif sets

pymnet: A Python Library for Multilayer Networks

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