# Applications of Network Theory: From Mechanisms to Large-Scale Structure

March 28, 2011 to April 20, 2011
Europe/Stockholm timezone

## Design robust network: how and why?

Apr 19, 2011, 1:30 PM
1h

### 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?

### Presentation materials

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