Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walks in directed modular networks   Because diffusion typically involves symmetric interactions, scant attention
has been focused on studying asymmetric cases. However, important networked
systems underlain by diffusion (e.g. cortical networks and WWW) are inherently
directed. In the case of undirected diffusion, it can be shown that the
steady-state probability of the random walk dynamics is fully correlated with
the degree, which no longer holds for directed networks. We investigate the
relationship between such probability and the inward node degree, which we call
efficiency, in modular networks. Our findings show that the efficiency of a
given community depends mostly on the balance between its ingoing and outgoing
connections. In addition, we derive analytical expressions to show that the
internal degree of the nodes do not play a crucial role in their efficiency,
when considering the Erd\H{o}s-R\'enyi and Barab\'asi-Albert models. The
results are illustrated with respect to the macaque cortical network, providing
subsidies for improving transportation and communication systems.

20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org