The recent trend of rapid urbanization makes it imperative to understand urban characteristics such as infrastructure, population distribution, jobs, and services that play a key role in urban livability and sustainability. A healthy debate exists on what constitutes optimal structure regarding livability in cities, interpolating, for instance, between mono- and poly-centric organization. Here anonymous and aggregated flows generated from three hundred million users, opted-in to Location History, are used to extract global Intra-urban trips. We develop a metric that allows us to classify cities and to establish a connection between mobility organization and key urban indicators. We demonstrate that cities with strong hierarchical mobility structure display an extensive use of public transport, higher levels of walkability, lower pollutant emissions per capita and better health indicators. Our framework outperforms previous metrics, is highly scalable and can be deployed with little cost, even in areas without resources for traditional data collection.

Pagerank, a network-based diffusion algorithm, has emerged as the leading method to rank web content, ecological species and even scientists. Despite its wide use, it remains unknown how the structure of the network on which it operates affects its performance. Here we show that for random networks the ranking provided by pagerank is sensitive to perturbations in the network topology, making it unreliable for incomplete or noisy systems. In contrast, in scale-free networks we predict analytically the emergence of super-stable nodes whose ranking is exceptionally stable to perturbations. We calculate the dependence of the number of super-stable nodes on network characteristics and demonstrate their presence in real networks, in agreement with the analytical predictions. These results not only deepen our understanding of the interplay between network topology and dynamical processes but also have implications in all areas where ranking has a role, from science to marketing.

In the last few years we have witnessed the emergence, primarily in online communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folksonomy, a tripartite structure of users, resources, and tags—labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures that represents them as random hypergraphs. We show that it is possible to calculate many properties of this model exactly in the limit of large network size and we compare the results against observations of a real folksonomy, that of the online photography website Flickr. We show that in some cases the model matches the properties of the observed network well, while in others there are significant differences, which we find to be attributable to the practice of multiple tagging, i.e., the application by a single user of many tags to one resource or one tag to many resources.

The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. Here we demonstrate that its statistical distribution is invariant for planar networks, that are used to model many infrastructural and biological systems. Empirical analysis of street networks from 97 cities worldwide, along with simulations of random planar graph models, indicates the observed invariance to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime corresponding to loops providing local path alternatives. Furthermore, the high betweenness nodes display a non-trivial spatial clustering with increasing spatial correlation as a function of the edge-density. Our results suggest that the spatial distribution of betweenness is a more accurate discriminator than its statistics for comparing static congestion patterns and its evolution across cities as demonstrated by analyzing 200 years of street data for Paris.