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We introduce a method that can be used to evolve the topology of a network ina way that preserves both the network's spectral as well as local structure.This method is quite versatile in the sense that it can be used to evolve anetwork's topology over any collection of the network's elements. Thisevolution preserves both the eigenvector centrality of these elements as wellas the eigenvalues of the original network. Although this method is introducedas a tool to model network growth, we show it can also be used to compare thetopology of different networks where two networks are considered similar iftheir evolved topologies are the same. Because this method preserves thespectral structure of a network, which is related to the network's dynamics, itcan also be used to study the interplay of network growth and function. We showthat if a network's dynamics is intrinsically stable, which is a strongerversion of the standard notion of stability, then the network remainsintrinsically stable as the network's topology evolves. This is of interestsince the growth of a network can have a destabilizing effect on the network'sdynamics, in general. In this sense the methods developed here can be used as atool for designing mechanisms of network growth that ensure a network remainsstabile as it grows.

Mechanisms for Network Growth that Preserve Spectral and Local Structure