Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growing Random Networks with Fitness   Three models of growing random networks with fitness dependent growth rates
are analysed using the rate equations for the distribution of their
connectivities. In the first model (A), a network is built by connecting
incoming nodes to nodes of connectivity $k$ and random additive fitness $\eta$,
with rate $(k-1)+ \eta $. For $\eta >0$ we find the connectivity distribution
is power law with exponent $\gamma=<\eta>+2$. In the second model (B), the
network is built by connecting nodes to nodes of connectivity $k$, random
additive fitness $\eta$ and random multiplicative fitness $\zeta$ with rate
$\zeta(k-1)+\eta$. This model also has a power law connectivity distribution,
but with an exponent which depends on the multiplicative fitness at each node.
In the third model (C), a directed graph is considered and is built by the
addition of nodes and the creation of links. A node with fitness $(\alpha,
\beta)$, $i$ incoming links and $j$ outgoing links gains a new incoming link
with rate $\alpha(i+1)$, and a new outgoing link with rate $\beta(j+1)$. The
distributions of the number of incoming and outgoing links both scale as power
laws, with inverse logarithmic corrections.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio