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This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
Modeling continuous-time dynamics constitutes a foundational challenge, and uncovering inter-component correlations within complex systems holds promise for enhancing the efficacy of dynamic modeling. The prevailing approach of integrating…
Are the embeddings of a graph's degenerate core stable? What happens to the embeddings of nodes in the degenerate core as we systematically remove periphery nodes (by repeated peeling off $k$-cores)? We discover three patterns w.r.t.…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
We study probabilistic protocols for concurrent threshold-based load balancing in networks. There are n resources or machines represented by nodes in an undirected graph and m >> n users that try to find an acceptable resource by moving…
We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of…
Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…
In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
As the scale of networked control systems increases and interactions between different subsystems become more sophisticated, questions of the resilience of such networks increase in importance. The need to redefine classical system and…
How the architecture of gene regulatory networks ultimately shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify non-random features in these…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
In this paper, we aim to find the conditions for input-state stability (ISS) and incremental input-state stability ($\delta$ISS) of Gated Graph Neural Networks (GGNNs). We show that this recurrent version of Graph Neural Networks (GNNs) can…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…