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In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is "aristocratic", since few elements "connect" the system, while a non-hyperbolic network has a more "democratic" structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an "influence area" for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define "local" networks (i.e., social or peer-to-peer networks), and large in "global" networks (i.e., power grid, metabolic networks, or autonomous system networks). [ABSTRACT FROM AUTHOR]

We analyze weighted networks as randomly reinforced urn processes, in which the edge-total weights are determined by a reinforcement mechanism. We develop a statistical test and a procedure based on it to study the evolution of networks over time, detecting the "dominance" of some edges with respect to the others and then assessing if a given instance of the network is taken at its steady state or not. Distance from the steady state can be considered as a measure of the relevance of the observed properties of the network. Our results are quite general, in the sense that they are not based on a particular probability distribution or functional form of the random weights. Moreover, the proposed tool can be applied also to dense networks, which have received little attention by the network community so far, since they are often problematic. We apply our procedure in the context of the International Trade Network, determining a core of "dominant edges." [ABSTRACT FROM AUTHOR]

This work analyzes methods for the identification and the stability under perturbation of a territorial community structure with specific reference to transportation networks. We considered networks of commuters for a city and an insular region. In both cases, we have studied the distribution of commuters' trips (i.e., home-to-work trips and vice versa). The identification and stability of the communities' cores are linked to the land-use distribution within the zone system, and therefore their proper definition may be useful to transport planners. [ABSTRACT FROM AUTHOR]