From social to neuronal, networks are omnipresent in our day-to-day lives. Networks such as transportation, power grids, web-pages, face book or internet are complex systems built up of a collection of similar objects with an underlying pattern in their interactions or relations. ‘This is true for natural numbers, too’, is the thought behind researchers applying complex networks to study patterns in numbers.

Using the framework of complex networks, IISER Pune researchers G. Ambika, Professor in Physics at IISER Pune; graduate student Snehal Shekatkar; and IISER Pune Math faculty member Chandrasheel Bhagwat have found a novel pattern in natural numbers based on the divisibility of the numbers (Nature Scientific Reports 2015:14280).
 

In a network of natural numbers generated by the team, each number was a node and two nodes were connected if one of them divides the other (for example, 3 and 12 would be connected but 3 and 14 will not be connected). Networks of different sizes were considered and their topological characteristics were studied and compared.

This analysis led them to an interesting observation: divisibility relations did not involve any characteristic scale but the characteristics of the network seemed to vary smoothly with the size of the network. This was surprising in view of the fact that distribution or occurrence of prime numbers has been known to be irregular in the sequence of natural numbers. There was an interesting similarity in the clustering properties of the network. The team named this new phenomenon as “stretching similarity”.

In a separate study supported by DST DAAD, Prof Ambika and Mr Shekatkar in collaboration with the research group of Prof Juergen Kurths from Potsdam Institute of Climate Impact Research, Germany have studied the connectivity patterns between airports in USA and Europe (Nature Scientific Reports 2015:18183). For this complex system of “network of networks”, the team came up with a relatively simple model called RAIN (RAndom Interacting Network) that predicts the dependence of international connections between Europe and USA, solely on the basis of domestic connections in these two regions. The RAIN model statistically relates intra-network features to inter-network structure and as such its framework is general and can be potentially adapted to various real-world complex systems.

- Reported by Shanti Kalipatnapu