Abstract by DJ Passey
The Specialization Model: Network Growth that Preserves Eigenvalues
The specialization model of network growth provides a way to grow a network so that the specialized network and the original network have the same eigenvalues. Networks grown via this process exhibit increases in modularity, sparsity and hierarchical structure found in gene regulatory networks, the brain and the internet. Networks generated using our model also demonstrate many well known properties of real-wold networks such as the small-world property, disassortativity, power-law like degree distributions and clustering coefficients.
The specialization of a network via our process completely preserves the network’s spectrum. This allows us to show that a network maintains certain dynamic proper- ties, specifically stability under mild conditions, as the network’s topology becomes increasingly complex due to specialization.
In addition to stability, specialization allows us to grow isolated components of the network. Using eigenvector centrality as a metric, we describe how the importance of these components evolves as they are specialized.