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In this paper, we address short cycle effects in the distributed low density generator matrix (LDGM) codes. As a codeword is formed from various nodes, the decentralized code construction makes it difficult to eliminate short cycles, resulting in a degraded code performance. To mitigate this effect, we propose a distributed algorithm which can eliminate short cycles within the network. The complexity of the proposed algorithm is a linear function of the number of relay nodes in the network. The simulation results show that the code performance can lower the error floor of irregular LDGM codes significantly, when all short cycles have been removed.