#19 Correlation and Connectivity in Spatial Networks: Exploring Patterns and Impacts

One fundamental characteristic of the structure of a given network is how its elements connect to each other. In social networks, for instance, it is common to find individuals with many connections being linked to other individuals with many connections. In other words, while it is very rare to find a low-popularity individual connected to a celebrity, it is highly likely that a given celebrity knows and interacts with other celebrities. In spatial embedded networks the opposite is generally observed. In a granular pack, such as in a sand pile or a coffee powder, smaller particles with fewer contacts tend to surround larger particles to maximize the occupied volume fraction. There is then a negative degree and size correlation between pairs of grains in contact. Such correlations are crucial to determine the overall behavior of the network, whether it be its resilience or its connectivity.

In this project, we will study different networks embedded in space and understand how different spatial organizations impose specific types of correlation on the overall structure of the network and the impacts on its large-scale behavior.