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J. (2002). The structure and function of networks. , Vol. 147, pp. 40-45 Newman, M. E. ; Strogatz, S. H. & Watts, D. J. (2001). Random graphs with arbitrary degree distributions and their applications. Physical Review E, Vol. 64 Orengo, C. ; Michie, A. ; Jones, D. T. ; Swindells, M. B. ~M. (1997). CATH - a hierarchic classification of protein domain structures. Structure, Vol. 5, pp. 1093-1108 Réka, A. -L. (2000). Topology of evolving networks: local events and universality. Physical Review Letters, Vol.
Where σuv is the number of shortest paths between the nodes u and v, and σuv (t) is the number of shortest paths between u to v that pass through t. The average betweenness of nodes interacting with other secondary structure motifs is shown on Fig 24. We can see that the average betweenness of the small-world networks is similar to the average betweenness of the other networks. This means that neither the quantity nor the quality of nodes that link different SSEs guarantees a short characteristic path length.
Fig. 20. Ratio of inter-SSE edges (r) as a function of the network size for the four classes of studied proteins. 3 Consequences During our study, we have identified a means to approximate the cumulative degree distribution of the SSE-IN. This function describes a power law regime followed by a sharp cut-off. The SSE-In studied are consequently truncated scale-free networks. The study of the hubs shows that certain amino acid play a central role independently of the protein classification. The nature of these hubs depends on their positions in the primary structure.