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The exponential growth in Internet traffic requires a high-capacity transmission platform and emphasizes the importance of a multi-granularity transport network due to heterogeneous connection requests. Elastic Optical Network has been considered as a promising solution because of large transport capacity and bandwidth flexibility. Routing and spectrum allocation is one of important problems in EON. However, with spectrum continuity constraint and contiguity constraint, the set-up and tear-down of light paths may cause fragmentation problem which refers to small-sized and uncontiguous spectrums. The fragmentation increases the connection blocking probability and decrease spectrum utilization. In this paper a novel routing and spectrum allocation algorithm is proposed to minimize fragmentation in EON. The proposed algorithm consists of routing problem and the spectrum allocation problem. In the first step, K-shortest paths algorithm is employed and candidate paths are found according to the distance between source and destination. In the second step, fragmentation-aware spectrum allocation algorithm is applied. We define block cost function to determine appropriate spectral block for connection request. The block cost function is based on the state of neighboring frequency slots to minimize the fragmentation after spectrum allocation. The performance of proposed algorithm is evaluated in terms of blocking probability and spectrum utilization.