  The load of a node in a network is the total traffic going through it when
every node pair sustains a uniform bidirectional traffic between them on
shortest paths. We show that nodal load can be expressed in terms of the more
elementary notion of a node's descents in breadth-first-search (BFS or
shortest-path) trees, and study both the descent and nodal-load distributions
in the case of scale-free networks. Our treatment is both semi-analytical
(combining a generating-function formalism with simulation-derived BFS
branching probabilities) and computational for the descent distribution; it is
exclusively computational in the case of the load distribution. Our main result
is that the load distribution, even though it can be disguised as a power-law
through subtle (but inappropriate) binning of the raw data, is in fact a
succession of sharply delineated probability peaks, each of which can be
clearly interpreted as a function of the underlying BFS descents. This find is
in stark contrast with previously held belief, based on which a power law of
exponent -2.2 was conjectured to be valid regardless of the exponent of the
power-law distribution of node degrees.
