On the renormalization of random network models

Catanzaro, A.

This thesis deals with the broad topic of renormalization of complex networks, with a particular focus on the topological nature of such models of complex systems. It is divided into two main parts.

In the first part, we discuss the characterization of the spectrum and the clustering function of a recently proposed network model with independent edges. This model can be regarded as the ’fixed point’ of a topology-preserving aggregation process that allows to deal with multi-scale clustered data. We investigate its properties in the regime where the node features are distributed according to an infinite-mean stable probability density function, making the model scale-invariant both in the functional form of the link probability and in the hidden variable distribution. In particular, in Chapter 2 we analyze the model spectral properties, while in Chapter 3 we discuss its clustering function.

In the second part, we elaborate on a specific...

This thesis deals with the broad topic of renormalization of complex networks, with a particular focus on the topological nature of such models of complex systems. It is divided into two main parts.

In the first part, we discuss the characterization of the spectrum and the clustering function of a recently proposed network model with independent edges. This model can be regarded as the ’fixed point’ of a topology-preserving aggregation process that allows to deal with multi-scale clustered data. We investigate its properties in the regime where the node features are distributed according to an infinite-mean stable probability density function, making the model scale-invariant both in the functional form of the link probability and in the hidden variable distribution. In particular, in Chapter 2 we analyze the model spectral properties, while in Chapter 3 we discuss its clustering function.

In the second part, we elaborate on a specific renormalization scheme that is equivalent to marginalization over disordered uncertainty, in the context of random network models that might display a correlation (possibly higher-order) among links. In particular in Chapter 4 we introduce the marginalization framework, and show two classes of effectively solvable models exist. In Chapter 5 we analyze in detail the first class of models that become solvable under the marginalization flow, and elaborate on its applications to temporal networks. Finally, in Chapter 6 we tackle the second class of those models, by providing a general solution framework for II order Random Network Models.

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On the renormalization of random network models