### Speaker

Prof.
Zhi-Xi Wu
(Lanzhou University)

### Description

In a recent PNAS paper (PNAS.108.3838: Mitigation of
malicious attach on network), Schneider et.al. introduced a
new measure for robustness of network to malicious attacks,
$R=1/N\sum_{q=1}^N s(q)$, where $N$ is the number of nodes
in the network and s(q) is the fraction of nodes in the
largest connected cluster after removing q nodes with
highest degree. In terms of the measurement R, the authors
proposed a way to improve the robustness of a network:
continuously swap the connections of two randomly chosen
edges to increase R until no further improvement is
achieved. It has been found that such manipulations are
efficient in improving the performance of the European
electricity system and the Internet as well as complex
networks models against malicious attacks. Particularly, in
the case of scale-free networks, a unique onion-like
topology characterizing robust networks is revealed.
However, we note that only connectivity links are considered
when disintegrating the network (a node fails only when it,
or the cluster it is in, becomes completely disconnected
from the network). Nonetheless, dependency links are more
relevant for real transmission systems, such as the power
grids and Internet traffic. That is, the nodes in the
networks are interdependent, and the failure of one node may
cause his direct neighbors to become also failure (with some
probability). Here we make comparative studies by
investigating cascading process on scale-free networks
generated by uncorrelated configuration model and the
optimal surrogates in terms of Schneider et.al. Our
preliminary simulations suggest that in the context of
cascading dynamics the onion-like topology may be rather
fragile to both random failures and intentional attacks as
compared to the original networks. As such, caution should
be taken into account in designing real infrastructures by
using the method presented in the PNAS paper, and an open
question therefore arises: how to design a robust network in
which the nodes are interdependent?