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We propose a degree-based coarse graining approach that not just accelerates the evaluation of dynamics on complex networks, but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions…
Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different…
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…
In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…
Given the prevalence of JPEG compressed images, optimizing image reconstruction from the compressed format remains an important problem. Instead of simply reconstructing a pixel block from the centers of indexed DCT coefficient quantization…
The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
The ability to control complex networks is of crucial importance across a wide range of applications in natural and engineering sciences. However, issues of both theoretical and numerical nature introduce fundamental limitations to…
Predicting future interactions or novel links in networks is an indispensable tool across diverse domains, including genetic research, online social networks, and recommendation systems. Among the numerous techniques developed for link…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric…
Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to…
We introduce root-to-leaf path random walks on double covers of graded signed graphs and analyze their behavior in a general setting. Viewing simplicial complexes within this framework, we show that these walks induce the natural…
We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…