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In this work we consider the topological analysis of symbolic formal systems in the framework of network theory. In particular we analyse the network extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the vertices…
Network science has experienced unprecedented rapid development in the past two decades. The network perspective has also been widely applied to explore various complex systems in great depth. In the first decade, fundamental…
The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
Coordinated human behaviour takes place within a diverse range of social organisational structures, which can be thought of as power structures with "managers" who influence "subordinates". A change in policy in one part of the organisation…
In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and to the fruitful application of powerful methods used in statistical…
This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to…
The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals…
Many real-world networks such as social networks consist of strategic agents. The topology of these networks often plays a crucial role in determining the ease and speed with which certain information driven tasks can be accomplished.…
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the…
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the…
Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Complex networks are used to depict topological features of complex systems. The structure of a network characterizes the interactions among elements of the system, and facilitates the study of many dynamical processes taking place on it.…