Daniel Grady

The Structure of Borders in a Small World

Territorial subdivisions and geographic borders are essential for understanding phenomena in sociology, political science, history, and economics. They influence the interregional flow of information and cross-border trade and affect the diffusion of innovation and technology. However, it is unclear if existing administrative subdivisions that typically evolved decades ago still reflect the most plausible organizational structure of today. The complexity of modern human communication, the ease of long-distance movement, and increased interaction across political borders complicate the operational definition and assessment of geographic borders that optimally reflect the multi-scale nature of todays human connectivity patterns. What border structures emerge directly from the interplay of scales in human interactions is an open question. Based on a massive proxy dataset, we analyze a multi-scale human mobility network and compute effective geographic borders inherent to human mobility patterns in the United States. We propose two computational techniques for extracting these borders and for quantifying their strength. We find that effective borders only partially overlap with existing administrative borders, and show that some of the strongest mobility borders exist in unexpected regions. We show that the observed structures cannot be generated by gravity models for human traffic. Finally, we introduce the concept of link significance that clarifies the observed structure of effective borders. Our approach represents a novel type of quantitative, comparative analysis framework for spatially embedded multi-scale interaction networks in general and may yield important insight into a multitude of spatiotemporal phenomena generated by human activity.

Robust classification of salient links in complex networks

Complex networks in natural, social and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods and concepts have been proposed to address this problem such as centrality statistics, motifs, community clusters and backbones, but such schemes typically rely on external and arbitrary parameters. It is unknown whether generic networks permit the classification of elements without external intervention. Here we show that link salience is a robust approach to classifying network elements based on a consensus estimate of all nodes. A wide range of empirical networks exhibit a natural, network-implicit classification of links into qualitatively distinct groups, and the salient skeletons have generic statistical properties. Salience also predicts essential features of contagion phenomena on networks, and points towards a better understanding of universal features in empirical networks that are masked by their complexity.

Eyjafjallajökull and 9/11: The impact of large-scale disasters on worldwide mobility

Large-scale disasters that interfere with globalized socio-technical infrastructure, such as mobility and transportation networks, trigger high socio-economic costs. Although the origin of such events is often geographically confined, their impact reverberates through entire networks in ways that are poorly understood, difficult to assess, and even more difficult to predict. We investigate how the eruption of volcano Eyjafjallajökull, the September 11th terrorist attacks, and geographical disruptions in general interfere with worldwide mobility. To do this we track changes in effective distance in the worldwide air transportation network from the perspective of individual airports. We find that universal features exist across these events: airport susceptibilities to regional disruptions follow similar, strongly heterogeneous distributions that lack a scale. On the other hand, airports are more uniformly susceptible to attacks that target the most important hubs in the network, exhibiting a well-defined scale. The statistical behavior of susceptibility can be characterized by a single scaling exponent. Using scaling arguments that capture the interplay between individual airport characteristics and the structural properties of routes we can recover the exponent for all types of disruption. We find that the same mechanisms responsible for efficient passenger flow may also keep the system in a vulnerable state. Our approach can be applied to understand the impact of large, correlated disruptions in financial systems, ecosystems and other systems with a complex interaction structure between heterogeneous components.

Modularity Maximization and Tree Clustering: Novel Ways to Determine Effective Geographic Borders

Territorial subdivisions and geographic borders are essential for understanding phenomena in sociology, political science, history, and economics. They influence the interregional flow of information and cross-border trade and affect the diffusion of innovation and technology. However, most existing administrative borders were determined by a variety of historic and political circumstances along with some degree of arbitrariness. Societies have changed drastically, and it is doubtful that currently existing borders reflect the most logical divisions. Fortunately, at this point in history we are in a position to actually measure some aspects of the geographic structure of society through human mobility. Large-scale transportation systems such as trains and airlines provide data about the number of people traveling between geographic locations, and many promising human mobility proxies are being discovered, such as cell phones, bank notes, and various online social networks. In this chapter we apply two optimization techniques to a human mobility proxy (bank note circulation) to investigate the effective geographic borders that emerge from a direct analysis of human mobility.