- Identifying functional modules or pathways in biological networks may help better understand the underlying cellular functional mechanisms. Different from traditional network module identification problems, biological modules often overlap with each other. However, existing functional module identification algorithms can only generate overlapping densely connected modules but ignore the modules within which the molecules rarely interact but have similar interaction patterns to the rest of the network. In this paper, we propose a novel overlapping functional module identification algorithm, which aims to detect overlapping modules by grouping molecules with similar interaction patterns and hence can generate both dense modules as well as sparse modules with biological meaning. We formulate this overlapping module identification problem by considering one-step and two-step Markov random walk (busy Markov random walk) on networks and solve it by an approximate spectral algorithm together with a bottom-up greedy strategy. The proposed algorithm P1P2 is shown to outperform a range of state-of-the-art overlapping module identification approaches on both overlapping benchmarks and real world PPI networks. 2013 IEEE.