Journal of Advances in Mathematics and Computer Science 24(1): 1-14, 2017; Article no.JAMCS.34933 Previously known as British Journal of Mathematics & Computer Science ISSN: 2231-0851 The Cycled Shortest Path Problem: A New Perspective, And Sensitivity Analysis Asghar Aini 1 ∗ , Kourosh Eshghi 1 and Amir Salehipour 2 1 Department of Industrial Engineering, Sharif University of Technology, Azadi Avenue, 14598, Tehran, Iran. 2 CARMA, The University of Newcastle NSW 2308, Australia. Authors’ contributions This work was carried out in collaboration between all authors. All authors equally contributed into the study. Author AA developed the major theoretical works. All authors read and approved the final manuscript. Article Information DOI: 10.9734/JAMCS/2017/34933 Editor(s): (1) Huchang Liao, Business School, Sichuan University, P. R. China. Reviewers: (1) K. Thilagam, Pondicherry Engineering College, India. (2) Y. Harold Robinson, Anna University, India. (3) Vikram Puri, GNDU Regional Campus Jalandhar, India. Complete Peer review History: http://www.sciencedomain.org/review-history/20610 Received: 20 th June 2017 Accepted: 30 th July 2017 Original Research Article Published: 22 nd August 2017 Abstract Several algorithms, including the Floyd-Warshall algorithm, have been developed to calculate the shortest path between every pair of vertices in a graph (network) with cycles. This study proposes an exact algorithm, the Cascade Rectangle (CR) algorithm, for calculating the shortest paths between every pair of vertices in cycled graphs. The algorithm is developed by designing and implementing certain improvements to the available exact algorithms. In particular, the proposed algorithm has an improved computational complexity, although its worst computational complexity is O(n 3 ). Moreover, the CR algorithm is easier to implement, which is an advantage for teaching and learning purposes. In addition to this, we introduce a new concept, the transposition matrix, which has important applications in sensitivity analysis and re-optimization of the shortest path networks. An example illustrates the CR algorithm and the new concept of transposition matrix. *Corresponding author: E-mail: ainiasghar@ie.sharif.edu;