A random interacting network model for complex networks (original) (raw)

We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate withinnetwork characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed internetwork assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems. Complex networks provide a powerful approach for investigating real-world systems. It helps us to understand phenomena observed over a wide range of disciplines such as biology, climate, environment, social sciences, technology, and economics 1-4. Many real-world networks, however, are composed of subnetworks called communities which are more closely connected within each other than to the rest of the network 5,6. In other cases, networks of one kind (e.g., a power grid) interact with networks of another kind (e.g., communications systems), leading to a necessary extension of the complex network paradigm that incorporates different types of networks with different types of interactions between them. Initial studies dealing with interdependent networks considered the interrelations between the Internet communication network and the power grid network 7,8. There have been similar studies in other fields since then: such as that of a network of networks in climate 9 where individual isobaric layers of the atmosphere were represented as a complex network with the different isobar networks connected among themselves, epidemic spreading on interconnected networks 10,11 , and that of the European air transportation multiplex network 12 , where each airline comprised a layer with the set of all airports forming a common set of nodes to all layers. For the purposes of this study, all such scenarios involving two or more networks, are examples of interacting networks. We use here the prefix intra-to denote quantities defined within a chosen subnetwork and the prefix inter-to denote quantities defined between subnetworks. While modeling interacting networks most studies use a rather simple interaction structure between the subnetworks even though the topology of each subnetwork is quite complex. This is in contrast to several real-world systems where the interactions between communities are extremely relevant and complex, such as in the brain 13,14. Moreover, a few studies have also indicated the influence of intra-network topology on the inter-network behavior 15-17. Keeping this in mind, we put forward a much more general model of interacting networks, i.e., a RAndom Interacting Network (RAIN) model, which should offer the following features: (i) it should be able to consider any given form of interaction of each subnetwork as well as of the interactions between the subnetworks, irrespective of its complexity, (ii) it should be able to consider the dependence (if any) of inter-network interaction on the