Related papers: Renormalization of Interacting Random Graph Models

This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be…

We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the…

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…

Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…

We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a…

The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…

We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that…

We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with…

I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…

In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…

We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally…

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…