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We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$.…
In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
To comprehend the multipartite organization of large-scale biological and social systems, we introduce a new information theoretic approach that reveals community structure in weighted and directed networks. The method decomposes a network…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…
A small-world topology characterizes many complex systems including the structural and functional organization of brain networks. The topology allows simultaneously for local and global efficiency in the interaction of the system…
Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…
Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features…
The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial…
Motivated by the empirical analysis of the air transportation system, we define a network model that includes geographical attributes along with topological and weight (traffic) properties. The introduction of geographical attributes is…
In this paper we derive a compact mathematical formulation describing the dynamics of chemical reaction networks that are complex-balanced and are governed by mass action kinetics. The formulation is based on the graph of (substrate and…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…