Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple structural transitions in interacting networks   Many real-world systems can be modeled as interconnected multilayer networks,
namely a set of networks interacting with each other. Here we present a
perturbative approach to study the properties of a general class of
interconnected networks as inter-network interactions are established. We
reveal multiple structural transitions for the algebraic connectivity of such
systems, between regimes in which each network layer keeps its independent
identity or drives diffusive processes over the whole system, thus generalizing
previous results reporting a single transition point. Furthermore we show that,
at first order in perturbation theory, the growth of the algebraic connectivity
of each layer depends only on the degree configuration of the interaction
network (projected on the respective Fiedler vector), and not on the actual
interaction topology. Our findings can have important implications in the
design of robust interconnected networked system, particularly in the presence
of network layers whose integrity is more crucial for the functioning of the
entire system. We finally show results of perturbation theory applied to the
adjacency matrix of the interconnected network, which can be useful to
characterize percolation processes on such systems.

33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th