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A central question of network science is how functional properties of systems arise from their structure. For networked dynamical systems, structure is typically quantified with network measures. A functional property that is of theoretical…
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
We consider the relation of symmetries and subspace controllability for spin networks with XXZ coupling subject to control of a single node by a local potential (Z-control). Such networks decompose into excitation subspaces. Focusing on the…
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…
In recent years complex networks have gained increasing attention in different fields of science and engineering. The problem of controlling these networks is an interesting and challenging problem to investigate. In this paper we look at…
In this paper, we study the continuous-time consensus problem in the presence of adversaries. The networked multi-agent system is modeled as a switched system, where the normal agents have integrator dynamics and the switching signal…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
In this work we present novel results to the problem of the Hegselmann-Krause dynamics in networks obtained by an extensive study of the behavior of the standard order parameter sensitive to the onset of consensus: the normalized size of…
Signed networks, i.e., networks with positive and negative edges, commonly arise in various domains from social media to epidemiology. Modeling signed networks has many practical applications, including the creation of synthetic data sets…
Controlling a complex network is of great importance in many applications. The network can be controlled by inputting external control signals through some selected nodes, which are called input nodes. Previous works found that the majority…
Multiagent systems consist of agents that locally exchange information through a physical network subject to a graph topology. Current control methods for networked multiagent systems assume the knowledge of graph topologies in order to…
In this note, we investigate the structural controllability and observability indices of structured systems. We provide counter-examples showing that an existing graph-theoretic characterization for the structural controllability index…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Signed networks appear naturally in contexts where conflict or animosity is apparent. In this book chapter we review some of the literature on signed networks, especially in the context of partitioning. Most of the work is founded in what…
We consider a nonlinear dynamical system on a signed graph, which can be interpreted as a mathematical model of social networks in which the links can have both positive and negative connotations. In accordance with a concept from social…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
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…
Better understanding our ability to control an interconnected system of entities has been one of the central challenges in network science. The theories of node and edge controllability have been the main methodologies suggested to find the…