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For that the existing community discovery algorithms of multi-layered social network (MSN) are lack and their results are crude, this paper presented cross-layer edge differential clustering coefficient(CLEDCC) algorithm in MSN based on edge clustering. This algorithm considered the strength of the relationships about any two nodes and their neighbors in each layer network, and respectively simulated for artificial sparse network, dense network and real datasets. Experimental results show that CLEDCC algorithm can effectively avoid the problem of parameter uncertainty, which is more accurate than the cross-layer edge clustering coefficient CLECC) algorithm in community discovery. [ABSTRACT FROM AUTHOR]