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Accueil du site > Séminaires > Séminaires 2019 > Small-world properties of Ulam Networks and reduced Google matrix for bank country interactions in Wikipedia.

Mardi 21 mai 2019 - 14:00

Small-world properties of Ulam Networks and reduced Google matrix for bank country interactions in Wikipedia.

Klaus Frahm (LPT Toulouse)

par Revaz Ramazashvili - 21 mai 2019

In the first part of the talk we analyze the small world properties of Ulam networks on examples of the Chirikov standard map and the Arnold cat map showing that the number of degrees of separation, or the Erdős number, grows logarithmically with the network size for the regime of strong chaos. This growth is related to the Lyapunov instability of chaotic dynamics. The presence of stability islands leads to an algebraic growth of the Erdős number with the network size.

In the second part we analyze the influence and interactions of 60 largest world banks for 195 world countries using the reduced Google matrix algorithm for the English Wikipedia network. While the top asset rank positions are taken by the banks of China we show that the network influence is dominated by US banks with Goldman Sachs being the central bank. We determine the effective friend/follower network structure of interactions of banks and countries as well as the PageRank sensitivity of countries to selected banks.

Post-scriptum :

contact : R. Ramazashvili