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Sizing Complex Networks

Friday, November 15, 2019


ISI seminar room 1st floor

Romain Brasselet Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy

Among the many features of natural and man-made complex networks the small-world phenomenon is a relevant and popular one. But, how small is a small-world network and how does it compare to others? Despite its importance, a reliable and comparable quantification of the average pathlength of networks has remained an open challenge over the years. Here, we uncover the upper (ultra-long) and the lower (ultra-short) limits for the pathlength and efficiency of networks. These results allow us to frame their length under a natural reference and to provide a synoptic representation, without the need to rely on the choice for a null-model (e.g., random graphs or ring lattices). Application to empirical examples of three categories (neural, social and transportation) shows that, while most real networks display a pathlength comparable to that of random graphs, when contrasted against the boundaries, only the cortical connectomes prove to be ultra-short.