Mapping networks in latent geometry: models and applications

Complex networks talk a common language, regardless of their origin, and are imprinted with universal features. Many of these features are well explained by the S1/H2 family of hidden metric space network models, where nodes are placed at specific coordinates in an underlying geometry, which led to the discovery that the effective geometry of many real networks is hyperbolic. Hyperbolicity emerges as a result of the combination of heterogeneous popularity and Euclidean similarity into an effective distance between nodes, such that more popular and similar nodes have more chance to interact. The geometric approach allows the production of truly cartographic maps of real networks in hyperbolic space that can be obtained using different techniques. Recently, we have introduced Mercator, an embedding tool that mixes machine learning and maximum likelihood approaches to perform dimensional reduction giving the coordinates of the nodes in the underlying hyperbolic disk with the best matching between the observed network topology and the underlying S1/H2 geometric model. The maps are not only visually appealing, but also meaningful and enable efficient navigation, the detection of communities of similar nodes, and a geometric renormalization group that unravels the multiple length scales coexisting in the structure of complex networks, strongly intertwined due to the small world property. The application of geometric renormalization to real networks unfolds them into a multilayer shell that shows scale invariance, meaning that the same principles are ruling the formation of network connections at different length scales. Interestingly, this self-similarity may have its origin in an evolutionary drive. Beyond its explanatory power, practical applications of the geometric renormalization technique include multiscale navigation and the production of downscaled or upscaled network replicas, among many other.

Maria Ángeles Serrano

Universitat de Barcelona, Spain

M. Ángeles Serrano obtained her Ph.D. in Physics at the Universitat de Barcelona in 1999 with a thesis about gravitational wave detection. One year later, she also received her Masters in Mathematics for Finance from the CRM-Universitat Autònoma de Barcelona. After four years in the private sector as IT consultant and mutual fund manager, she returned to academia in 2004 to work in the field of complex networks. She completed her postdoctoral research at Indiana University (USA), the École Polytechnique Fédérale de Lausanne (Switzerland) and IFISC Institute (Spain). She came back to Barcelona in 2009, when she was awarded a Ramón y Cajal Fellowship at UB. In February 2009, she obtained the Outstanding Referee award of the American Physical Society. She is a Founder Member of Complexitat, the Catalan Network for the study of Complex Systems, and a Promoter Member of UBICS, the Universitat de Barcelona Institute of Complex Systems. M. Ángeles Serrano is ICREA Research Professor at the Universitat de Barcelona from October 2015.


Wikimedia Public (Research) Resources

The Wikimedia Foundation's mission is to disseminate open knowledge effectively and globally. In keeping with this mission, the Wikimedia Foundation support research in areas that benefit the Wikimedia community. We aim to make any work with our support openly available to the public. At the same time that we do a minimalist user data collection, all the material (text and multimedia) available in our projects is public and reusable by everybody. Moreover, all the article versions and interactions among users are also public, and we offer a set of tools for accessing such data. In this tutorial we are going to give an overview on all the data sources, and a detailed explanation of how to interact with this content, including data and tools such as the Wikipedia Dumps, Quarry (SQL Replicas), Pageviews, PAWS (Jupyter Public Notebooks), Wikimedia Commons (multimedia content) and WikiData.

Diego Saez-Trumper

Wikimedia Foundation

Diego Sáez-Trumper is a Research Scientist at Wikimedia Foundation. Before, he was a post-doctoral researcher at Yahoo! Labs (Barcelona), Senior Research Scientist at Eurecat , Data Scientist at NTENT, and part time lecturer at UPF. He holds a diploma on Acoustic Engineering (Universidad Austral de Chile, 2006) and obtained his Phd in Information Technology from Universitat Pompeu Fabra (2013) under the supervision of Dr. Ricardo Baeza-Yates. During his PhD he interned at Qatar Computing Research Institute (2013), University of Cambridge (2012) and Universidade Federal de Minas Gerais (2011). His research interests include: Diffusion of information, innovation, and influence in online social networks; User modeling; Free knowledge; Relationship between social and mainstream media; Algorithms on graphs; and privacy issues.