The iterated local transitivity model for hypergraphs

Complex networks are pervasive in the real world, capturing dyadic interactions between pairs of vertices, and a large corpus has emerged on their mining modeling. However, many phenomena comprised polyadic more than two vertices. Such complex hypergraphs range from emails among groups individuals, scholarly collaboration, or joint proteins living cells. models form an emergent topic, requiring new techniques. A key generative principle within social other is transitivity, where friends likely friends. The previously proposed Iterated Local Transitivity (ILT) model incorporated transitivity as evolutionary mechanism. ILT provably satisfies observed properties networks, such densification, low average distances, high clustering coefficients. We propose new, for based called Hypergraph (or ILTH) model. In ILTH, we iteratively apply to hypergraphs. resulting generates simulating real-world hypergraphs, densification distances. consider unique not captured by 2-section. show that certain motifs, which specified subhypergraphs small order, have faster growth rates ILTH random with same order expected degree. graphs admitting homomorphism into 2-section initial hypergraph appear induced subgraphs existing coefficients, these coefficients larger values comparable