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In this paper, we present the empirical investigation results on the urban public transport networks (PTNs) and propose a model to understand the results obtained. We investigate some urban public traffic networks in China, which are the urban public traffic networks of Beijing, Guangzhou, Wuhan and etc. The empirical results on the big cities show that the accumulative act-degree distributions of PTNs take neither power function forms, nor exponential function forms, but they are described by a shifted power function, and the accumulative act-degree distributions of PTNs in medium-sized or small cities follow the same law. In the end, we propose a model to show a possible evolutionary mechanism for the emergence of such network. The analytic results obtained from this model are in good agreement with the empirical results. [ABSTRACT FROM AUTHOR]