Figure 1
From: Scaling in complex systems: a link between the dynamics of networks and growing interfaces
Illustration of the visibility algorithm that converts for each time step a growing interface into a complex network.
Left: A growing interface on a substrate of size L at four times. It can be described by a continuous function, h(x, t) which represents the height of point or angle x at time t. Middle: An interface is represented at any time of its evolution by a corresponding complex network by applying the visibility algorithm and which is formed with the same number of nodes N as the interface length L. A point of the interface is considered as a node in the visibility graph which is connected to those nodes that are visible from its heights h. Right: Based on the connectivity of each node, ki, we present an schematic visualization of the networks corresponding to the interfaces of the MBE dynamics at four different times under the k-core representation, which enables to disentangle the hierarchical structure of the networks by progressively focusing on their central cores.
