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Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
The robustness of complex networks was one of the first phenomena studied after the inception of network science. However, many contemporary presentations of this theory do not go beyond the original papers. Here we revisit this topic with…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…
The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used…
Advances in simultaneous recordings of large numbers of neurons have driven significant interest in the structure of neural population activity such as dimension. A key question is how these dynamic features arise mechanistically and their…
The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
We investigate the role of connection density in an adaptive network model of chaotic units that dynamically rewire based on their internal states and local coherence. By systematically varying the network's connectivity density, we uncover…
Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world…
We study the coevolution of network structure and signaling behavior. We model agents who can preferentially associate with others in a dynamic network while they also learn to play a simple sender-receiver game. We have four major…
What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents,…
Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…
Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is…