Preferential attachment and power-law degree distributions in heterogeneous multilayer hypergraphs

TL;DR

This paper models multilayer hypergraphs with complex, heterogeneous connectivity using preferential attachment, predicting universal power-law degree distributions across layers and hyperlink orders based on node types.

Contribution

It introduces a generalized preferential attachment model for multilayer hypergraphs with heterogeneity, deriving conditions for power-law degree distributions.

Findings

Power-law hyperdegree distributions are predicted for all node classes and layers.

The power-law exponent is universal across layers and hyperlink orders, depending only on node type.

The model accounts for complex connectivity structures and heterogeneity in multilayer hypergraphs.

Abstract

We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of acquiring a new hyperlink depends linearly on the vector of hyperdegrees of the node across all layers, as well as on the layer of the new hyperlink and the features of both linked nodes. We derive the consistency conditions that imply a power-law hyperdegree distribution for each class of nodes within each layer and of any order. For generic connectivity structures, we predict that the exponent of the power-law distribution is universal for all layers and all orders of hyperlinks, and it depends exclusively on the type of node.