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From trees to graphs: collapsing continuous-time branching processes. (arXiv:1711.03358v1 [math.PR])
来源于:arXiv
Continuous-time branching processes (CTBPs) are powerful tools in random
graph theory, but are not appropriate to describe real-world networks, since
they produce trees rather than (multi)graphs. In this paper we analyze
collapsed branching processes (CBPs), obtained by a collapsing procedure on
CTBPs, in order to define multigraphs where vertices have fixed out-degree
$m\geq 2$. A key example consists of preferential attachment models (PAMs), as
well as generalized PAMs where vertices are chosen according to their degree
and age. We identify the degree distribution of CBPs, showing that it is
closely related to the limiting distribution of the CTBP before collapsing. In
particular, this is the first time that CTBPs are used to investigate the
degree distribution of PAMs beyond the tree setting. 查看全文>>