Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Network Reliability: The effect of local network structure on diffusive
  processes   This paper re-introduces the network reliability polynomial - introduced by
Moore and Shannon in 1956 -- for studying the effect of network structure on
the spread of diseases. We exhibit a representation of the polynomial that is
well-suited for estimation by distributed simulation. We describe a collection
of graphs derived from Erd\H{o}s-R\'enyi and scale-free-like random graphs in
which we have manipulated assortativity-by-degree and the number of triangles.
We evaluate the network reliability for all these graphs under a reliability
rule that is related to the expected size of a connected component. Through
these extensive simulations, we show that for positively or neutrally
assortative graphs, swapping edges to increase the number of triangles does not
increase the network reliability. Also, positively assortative graphs are more
reliable than neutral or disassortative graphs with the same number of edges.
Moreover, we show the combined effect of both assortativity-by-degree and the
presence of triangles on the critical point and the size of the smallest
subgraph that is reliable.

25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an