Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized $k$-core pruning process on directed networks   The resilience of a complex interconnected system concerns the size of the
macroscopic functioning node clusters after external perturbations based on a
random or designed scheme. For a representation of the interconnected systems
with directional or asymmetrical interactions among constituents, the directed
network is a convenient choice. Yet how the interaction directions affect the
network resilience still lacks thorough exploration. Here, we study the
resilience of directed networks with a generalized $k$-core pruning process as
a simple failure procedure based on both the in- and out-degrees of nodes, in
which any node with an in-degree $< k_{in}$ or an out-degree $< k_{ou}$ is
removed iteratively. With an explicitly analytical framework, we can predict
the relative sizes of residual node clusters on uncorrelated directed random
graphs. We show that the discontinuous transitions rise for cases with $k_{in}
\geq 2$ or $k_{ou} \geq 2$, and the unidirectional interactions among nodes
drive the networks more vulnerable against perturbations based on in- and
out-degrees separately.

13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg