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There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…
Deep Graph Networks (DGNs) currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…
We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…
In a signed graph $G$, an induced subgraph is called a negative clique if it is a complete graph and all of its edges are negative. In this paper, we give the characteristic polynomials and the eigenvalues of some signed graphs having…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles,…
We start up the study of the stability of general graph pairs. This notion is a generalization of the concept of the stability of graphs. We say that a pair of graphs $(\Gamma,\Sigma)$ is stable if $Aut(\Gamma\times\Sigma) \cong…
Nonlinear network dynamics are notoriously difficult to understand. Here we study a class of recurrent neural networks called combinatorial threshold-linear networks (CTLNs) whose dynamics are determined by the structure of a directed…
Signed networks are graphs whose edges are labelled with either a positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The concept of balance in signed graph theory…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…
We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node…
Graph convolutional networks (GCNs) have emerged as powerful models for graph learning tasks, exhibiting promising performance in various domains. While their empirical success is evident, there is a growing need to understand their…