Abstract
This chapter deals with the study of some new properties of the intrinsic order graph. The intrinsic order graph is the natural graphical representation of a complex stochastic Boolean system (CSBS). A CSBS is a system depending on an arbitrarily large number \(n\) of mutually independent random Boolean variables. The intrinsic order graph displays its \(2^{n}\) vertices (associated to the CSBS) from top to bottom, in decreasing order of their occurrence probabilities. New relations between the intrinsic ordering and the Hamming weight (i.e., the number of \(1\)-bits in a binary \(n\)-tuple) are derived. Further, the distribution of the weights of the \(2^{n}\) nodes in the intrinsic order graph is analyzed.
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Acknowledgments
This work was supported in part by the “Ministerio de Economía y Competitividad” (Spanish Government), and FEDER, through Grant contract: CGL2011-29396-C03-01.
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González, L. (2013). Labeling the Nodes in the Intrinsic Order Graph with Their Weights. In: Yang, GC., Ao, Sl., Gelman, L. (eds) IAENG Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 229. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6190-2_40
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DOI: https://doi.org/10.1007/978-94-007-6190-2_40
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