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Algebraic Graph Theory for Sparse Flexibility Matrices

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Journal of Mathematical Modelling and Algorithms

Abstract

An efficient algorithm is presented for the formation of suboptimal cycle bases of graphs corresponding to sparse cycle adjacency matrices, leading to the formation of highly sparse flexibility matrices. The algorithm presented employs concepts from algebraic graph theory together with a Greedy-type algorithm to select cycles with small overlaps and uses a simple graph-theoretical method for controlling the independence of the selected cycles.

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References

  1. Kaveh, A.: Structural Mechanics: Graph and Matrix Methods, 2nd edn, Research Studies Press (Wiley), London, 1995.

    Google Scholar 

  2. Horton, J. D.: A polynomial time algorithm to find the shortest cycle basis of a graph, SIAM J. Comput. 16 (1987), 358–366.

    Google Scholar 

  3. Kaveh, A. and Roosta, G. R.: Revised Greedy Algorithm for the formation of a minimal cycle basis of a graph, Comm. Appl. Numer. Methods 10 (1994), 523–530.

    Google Scholar 

  4. Kaveh, A.: Improved cycle bases for the flexibility analysis of structures, Comput. Methods Appl. Mech. Enging 9 (1976), 267–272.

    Google Scholar 

  5. Kaveh, A.: Optimal Structural Analysis, Research Studies Press (Wiley), London, 1997.

    Google Scholar 

  6. Kaveh, A.: Suboptimal cycle bases of graphs for the flexibility analysis of skeletal structures, Comput. Methods Appl. Mech. Enging. 71 (1988), 259–271.

    Google Scholar 

  7. Kaveh, A.: Suboptimal cycle bases of a graph for mesh analysis of networks, Internat. J. NETWORKS 19 (1989), 273–279.

    Google Scholar 

  8. Henderson, J. C. de C. and Maunder, E. W. A.: A problem in applied topology, J. Inst. Math. Appl. 5 (1969), 254–269.

    Google Scholar 

  9. Gould, P.: The geographical interpretation of eigenvalues, Trans. Inst. British Geogr. 42 (1967), 53–58.

    Google Scholar 

  10. Straffing, P. D.: Linear algebra in geography, eigenvectors of networks, Math. Magazine 53 (1983), 355–362.

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Iran University of Science and Technology, Tehran-, 16, Iran

    A. Kaveh & H. Rahami

Authors
  1. A. Kaveh
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  2. H. Rahami
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Kaveh, A., Rahami, H. Algebraic Graph Theory for Sparse Flexibility Matrices. Journal of Mathematical Modelling and Algorithms 2, 171–182 (2003). https://doi.org/10.1023/A:1024977604724

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  • DOI: https://doi.org/10.1023/A:1024977604724

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