Investigating randomness in multiplex networks and hypergraphs

Abstract

While studying real-world systems whether it is biological, technological, social, physical, or otherwise, there is one thing common that pair-wise relationship between distinct elementary units in the system direct its structure and dynamics. For example, electric power transmission across several countries occurs between pairs of power stations. Correlation among the dipole moments of atomic spin pairs drives the magnetic phenomena in materials. The spread of diseases or ideas takes place amid the population by contacts between pairs of people. In international trade, the purchase and sale of goods and services happens by companies between pair of countries. And cellular processes in organisms pass on by interactions between pairs of proteins. The enumeration keeps going. Networks, basically a collection of individual units or nodes connected via pairwise links, known as edges reflects the idea of dependence between entities in pairs, making networks a valuable representation for various real-world systems.