In elastic optical networks, a connection uses different spectrum widths that spread over adjacent frequency slot units (FSUs) to improve utilization efficiency. A three-stage wavelength-space-wavelength (W-S-W) optical node architecture for elastic optical networks employs wavelength switching in the first and third stages and space switching in the second stage. This paper considers two W-S-W architectures, called WSW1 and WSW2 networks. In an earlier study, a matrix decomposition approach was used to derive a condition that was sufficient for rearrangeable nonblocking (RNB), but only for a WSW1 network with a limited number of connection rates. In this paper, instead of using a matrix decomposition approach, we use a graph approach to derive the same result. Furthermore, we adopt different graph approaches to derive two sufficient conditions, which benefit limited connection rates and limited input/output fibers of an RNB WSW1 (or WSW2) network. Specifically, the former is better than the latter if the number of connection rates is less than the minimum ceiling value of half the number of 1) input/output switches and 2) FSUs in each input and output fiber, and vice versa if the number of input/output switches is less than the minimum value of 1) twice the maximum FSUs occupied by a single connection and 2) FSUs in each input and output fiber. Note that limited input/output switches lead to limited input/output fibers. The graph approaches proposed in this paper can be applied to various other elastic optical networks for further study.
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2 July 2018: A typographical correction was made to page 679.
10 July 2018: A correction was made to the acknowledgment section.
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