Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Understanding the temporal pattern of spreading in heterogeneous
  networks: Theory of the mean infection time   For a reliable prediction of an epidemic or information spreading pattern in
complex systems, well-defined measures are essential. In the
susceptible-infected model on heterogeneous networks, the cluster of infected
nodes in the intermediate-time regime exhibits too large fluctuation in size to
use its mean size as a representative value. The cluster size follows quite a
broad distribution, which is shown to be derived from the variation of the
cluster size with the time when a hub node was first infected. On the contrary,
the distribution of the time taken to infect a given number of nodes is well
concentrated at its mean, suggesting the mean infection time is a better
measure. We show that the mean infection time can be evaluated by using the
scaling behaviors of the boundary area of the infected cluster and use it to
find a non-exponential but algebraic spreading phase in the intermediate stage
on strongly heterogeneous networks. Such slow spreading originates in only
small-degree nodes left susceptible, while most hub nodes are already infected
in the early exponential-spreading stage. Our results offer a way to detour
around large statistical fluctuations and quantify reliably the temporal
pattern of spread under structural heterogeneity.

5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
16
The categories of this paper are: stat
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int