Just as the name implies, complex networks are complex, and there are two different approaches for handling them. For statistical models on systems that cannot be solved exactly, we can (1) solve part of the problem and approximate the rest or (2) change the problem so that it can be solved exactly. My research focuses on the latter approach by using Hanoi networks to understand the relationship between the topology of a network and its phase behavior.
HNs are composed of a one-dimensional backbone chain with regular repeating long-range interactions. After assigning an integer label to each node, the long-range interactions are determined by how many times that integer is divisible by two. Slight variations of this method give rise to several different complex networks labeled by their average degree of connectivity—HN-3, HN-NP (non-planar), HN-5, and HN-6.