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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 nodes 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.
In this letter, we proposed an ungrowing scale-free network model, wherein the total number of nodes is fixed and the evolution of network structure is driven by a rewiring process only. In spite of the idiographic form of $G$, by using a two-order m
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a network in wh
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as possible. By appl
$Range$ and $load$ play keys on the problem of attacking on links in random scale-free (RSF) networks. In this Brief Report we obtain the relation between $range$ and $load$ in RSF networks analytically by the generating function theory, and then giv