We analyze the spreading patterns of COVID-19 outbreaks in different countries.

Propinquity Model

In the majority of network growth models, new nodes attach themselves to one or more existing nodes. Our propinquity model is based on the assumption that the selection of the second connection can be correlated to the position of the first connection. By varying the strength of this correlation, we can reproduce a variety of network structures and we can additionally tune the local density of the network.

Self-healing

The destruction of networks is well-understood, mainly through percolation concepts. The status of a network after destruction, though, is largely unexplored. We demonstrated that the isolated clusters remain quite close to each other and it is relatively easy to restore connectivity based on decisions made strictly on local information and minimal cost.

Network comparison

There are many practical applications where we want to compare two structures, such as complex networks. We proposed a method where we sample two networks at a given scale and compare the link density distribution at this scale. The method works very well, and can be used to identify effective classifiers.

What are our motivations in choosing our online friends? In our recent paper we study high-quality data and show how we can estimate the influence of different social drivers. In simpler words, how probable is it that we reply to friend requests or how often do we connect to popular people? Although we may not realize this, our connections evolve and we may find ourselves in an environment different from our choices.

We recently finished a work on how obesity, health indicators, economic indicators, etc spread geographically. For obesity, we find strong spatial correlations that extend up to 1000 miles. This suggests that the obesity epidemic is a collective phenomenon.

Brain presents a conundrum: we need isolated modules to process information, but this should all result in one unified picture. Our network analysis of fMRI data suggests that brain modules are fractal (large-world) but they are connected through lower-strength connections, that result in a global small-world network. This is a concept similar with Granovetter's 'strength of the weak ties' in social networks.

You want to spread a message in a social network. What would be your choice of the starting point for more efficient spreading? Surprisingly, it is not always the most connected individual; location can be more important than the number of connections.