Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Master equation for the degree distribution of a Duplication and
  Divergence network   Network growth as described by the Duplication-Divergence model proposes a
simple general idea for the evolution dynamics of natural networks. In
particular it is an alternative to the well known Barab\'asi-Albert model when
applied to protein-protein interaction networks. In this work we derive a
master equation for the node degree distribution of networks growing via
Duplication and Divergence and we obtain an expression for the total number of
links and for the degree distribution as a function of the number of nodes.
Using algebra tools we investigate the degree distribution asymptotic behavior.
Analytic results show that the network nodes average degree converges if the
total mutation rate is greater than 0.5 and diverges otherwise. Treating
original and duplicated node mutation rates as independent parameters has no
effect on this result. However, difference in these parameters results in a
slower rate of convergence and in different degree distributions. The more
different these parameters are, the denser the tail of the distribution. We
compare the solutions obtained with simulated networks. These results are in
good agreement with the expected values from the derived expressions. The
method developed is a robust tool to investigate other models for network
growing dynamics.

19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th