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Abstract: The load of a node in a network is the total traffic going through it whenevery node pair sustains a uniform bidirectional traffic between them onshortest paths. We show that nodal load can be expressed in terms of the moreelementary notion of a node-s descents in breadth-first-search BFS orshortest-path trees, and study both the descent and nodal-load distributionsin the case of scale-free networks. Our treatment is both semi-analyticalcombining a generating-function formalism with simulation-derived BFSbranching probabilities and computational for the descent distribution; it isexclusively computational in the case of the load distribution. Our main resultis that the load distribution, even though it can be disguised as a power-lawthrough subtle but inappropriate binning of the raw data, is in fact asuccession of sharply delineated probability peaks, each of which can beclearly interpreted as a function of the underlying BFS descents. This find isin stark contrast with previously held belief, based on which a power law ofexponent -2.2 was conjectured to be valid regardless of the exponent of thepower-law distribution of node degrees.



Author: Elias Bareinboim, Valmir C. Barbosa

Source: https://arxiv.org/







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