Dependence of Connectivity on the Logarithm of Geometric Distance in Brain Networks

Physical connections between nodes in a complex network are constrained by limiting factors such as the cost of establishing links and maintaining them, which can hinder network capability in terms of signal propagation speed and processing power. Trade-off mechanisms between cost constraints and performance requirements are reflected in the topology of a network and, ultimately, on the dependence of connectivity on geometric distance. This issue, though rarely addressed, is crucial in neuroscience, where physical links between brain regions are associated with a metabolic cost. In this work we investigate brain connectivity---estimated by means of a recently developed method that evaluates time scales of cross-correlation observability---and its dependence on geometric distance by analyzing resting state magnetoencephalographic recordings collected from a large set of healthy subjects. We identify three regimes of distance each showing a specific behaviour of connectivity. This identification makes up a new tool to study the mechanisms underlying network formation and sustainment, with possible applications to the investigation of neuroscientific issues such as aging and neurodegenerative diseases.