This article proposes a method to quantify the structure of a bipartite graph with a network entropy from a statistical-physical point of view . The network entropy of a bipartite graph with random links is computed from numerical simulation . As an application of the proposed method to analyze collective behavior, the affairs in which participants quote and trade in the foreign exchange market are quantified. The network entropy per node is found to correspond to the macroeconomic situation. A finite mixture of Gumbel distributions is used to fit with the empirical distribution for the minimum values of network entropy per node in each week. The mixture of Gumbel distributions with parameter estimates by segmentation procedure is verified by Kolmogorov-Smirnov test. The finite mixture of Gumbel distributions can extrapolate the probability of extreme events that have never been observed .
This article proposes a method to quantify the structure of a bipartite graph using a network entropy per link . The network entropy of a bipartite graph with random links is calculated both numerically and theoretically . As an application of the proposed method to analyze collective behavior, the affairs in which participants quote and trade in the foreign exchange market are quantified. The network entropy per link is found to correspond to the macroeconomic situation. A finite mixture of Gumbel distributions is used to fit the empirical distribution for the minimum values of network entropy per link in each week. The mixture of Gumbel distributions with parameter estimates by segmentation procedure is verified by the Kolmogorov--Smirnov test. The finite mixture of Gumbel distributions that extrapolate the empirical probability of extreme events has explanatory power at a statistically significant level .
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