60,540 research outputs found
The Configuration Model for Partially Directed Graphs
The configuration model was originally defined for undirected networks and
has recently been extended to directed networks. Many empirical networks are
however neither undirected nor completely directed, but instead usually
partially directed meaning that certain edges are directed and others are
undirected. In the paper we define a configuration model for such networks
where nodes have in-, out-, and undirected degrees that may be dependent. We
prove conditions under which the resulting degree distributions converge to the
intended degree distributions. The new model is shown to better approximate
several empirical networks compared to undirected and completely directed
networks.Comment: 19 pages, 3 figures, 2 table
Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade
We exploit the symmetry concepts developed in the companion review of this
article to introduce a stochastic version of link reversal symmetry, which
leads to an improved understanding of the reciprocity of directed networks. We
apply our formalism to the international trade network and show that a strong
embedding in economic space determines particular symmetries of the network,
while the observed evolution of reciprocity is consistent with a symmetry
breaking taking place in production space. Our results show that networks can
be strongly affected by symmetry-breaking phenomena occurring in embedding
spaces, and that stochastic network symmetries can successfully suggest, or
rule out, possible underlying mechanisms.Comment: Final accepted versio
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