<i>P</i>_<i>cum</i> distribution of subways, transportation and social networks.

Abstract

<p>The log-log plots of the cumulative degree distributions <i>P</i>_<i>cum</i>(<i>k</i>) of subways (Boston, Milan, New York, Paris, a to d), the US airline (e) and city-based online social networks (letter f to j) of Italy, Australia, The Netherlands, India and the United Kingdom. The distributions are characterized by exponents <i>γ</i> of <i>P</i>(<i>k</i>) ∼ <i>k</i>^−<i>γ</i> that is one plus the slope of <i>P</i>_<i>cum</i>(<i>k</i>) (in a log-log plot), i.e. <i>γ</i> = 1 + <i>γ</i>_<i>cum</i>. The coefficient is <i>γ</i> = 3.5 for subways networks, 2.6 for the US airline, 1.85 for Indian city-based online social network, 1.68 for the United Kingdom, 2.61 for Italy, 1.94 for Australia and 1.61 for the Netherlands. The coefficients for subways might not be precise due to the small dimension of the networks.</p