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    Network Geometry and Complexity 
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    Network Geometry and Complexity

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    Accepted version
    Embargoed until: 2019-07-02
    Reason: Publisher Embargo
    Volume
    173
    Pagination
    783 - 805
    Publisher
    Springer Verlag
    DOI
    10.1007/s10955-018-2115-9
    Journal
    Journal of Statistical Physics
    ISSN
    1572-9613
    Metadata
    Show full item record
    Abstract
    Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. More in general, higher-order networks can be cell-complexes formed by gluing convex polytopes along their faces. Interestingly, higher order networks have a natural geometric interpretation and therefore constitute a natural way to explore the discrete network geometry of complex networks. Here we investigate the rich interplay between emergent network geometry of higher order networks and their complexity in the framework of a non-equilibrium model called Network Geometry with Flavor. This model, originally proposed for capturing the evolution of simplicial complexes, is here extended to cell-complexes formed by subsequently gluing different copies of an arbitrary regular polytope. We reveal the interplay between complexity and geometry of the higher order networks generated by the model by studying the emergent community structure and the degree distribution as a function of the regular polytope forming its building blocks. Additionally, we discuss the underlying hyperbolic nature of the emergent geometry and we relate the spectral dimension of the higher-order network to the dimension and nature of its building blocks.
    Authors
    MULDER, D; Bianconi, G
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/42066
    Collections
    • Applied Mathematics [139]
    Licence information
    This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of Statistical Physics following peer review.
    Copyright statements
    © 2018 Springer Nature Switzerland AG. Part of Springer Nature.
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