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About this paper
Sanjukta Krishnagopal, Ginestra Bianconi
The authors present a spectral method for communities of simplices and a label-informed procedure for selecting higher-order interactions from pairwise data. Boundary matrices and Hodge Laplacians identify localized supports of simplex communities. On the Zachary Karate Club, removing triangle 2-8-32 gave the highest AMI among configurations, but label-guided selection does not establish the true interaction or generalize to unknown partitions.
Key insights
- The spectrum of the Hodge Laplacian directly encodes information about higher-order community structures, with non-zero eigenvectors localizing on $k$-simplicial communities.
- Higher-order interactions can be effectively inferred from pairwise network data by optimizing community detection performance against ground-truth information, demonstrating which multi-way interactions are truly relevant.
- Simplicial communities can exhibit 'persistence' across different interaction strength thresholds, revealing robust and scale-independent organizational features within complex systems.
Summary by alphaXiv.
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