Community structure detection in the evolution of the United States airport network

This is the post-print version of the Article. Copyright © 2013 World Scientific PublishingThis paper investigates community structure in the US Airport Network as it evolved from 1990 to 2010 by looking at six bi-monthly intervals in 1990, 2000 and 2010, using data obtained from the Bureau of Transportation Statistics of the US Department of Transport. The data contained monthly records of origin-destination pairs of domestic airports and the number of passengers carried. The topological properties and the volume of people traveling are both studied in detail, revealing high heterogeneity in space and time. A recently developed community structure detection method, accounting for the spatial nature of these networks, is applied and reveals a picture of the communities within. The patterns of communities plotted for each bi-monthly interval reveal some interesting seasonal variations of passenger flows and airport clusters that do not occupy a single US region. The long-term evolution of the network between those years is explored and found to have consistently improved its stability. The more recent structure of the network (2010) is compared with migration patterns among the four US macro-regions (West, Midwest, Northeast and South) in order to identify possible relationships and the results highlight a clear overlap between US domestic air travel and migration

Complex networks analysis in socioeconomic models

This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary adds insights on the statistical mechanical approach, and on the most relevant computational aspects for the treatment of these systems. As the most frequently used model for interacting agent-based systems, a brief description of the statistical mechanics of the classical Ising model on regular lattices, together with recent extensions of the same model on small-world Watts-Strogatz and scale-free Albert-Barabasi complex networks is included. Other sections of the chapter are devoted to applications of complex networks to economics, finance, spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issues, including results for opinion and citation networks. Finally, some avenues for future research are introduced before summarizing the main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared for Complexity and Geographical Economics - Topics and Tools, P. Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published

Hearing the clusters in a graph: A distributed algorithm

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies

Master stability functions reveal diffusion-driven pattern formation in networks

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space.For illustration we consider a generalized model of ecological meta-foodwebs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.Comment: 20 pages, 5 figures, to appear in Phys. Rev. E (2018