Abstract
Network robustness is the ability of a network to maintain a certain level of structural integrity and its original functions after being attacked, and it is the key to whether the damaged network can continue to operate normally. We define two types of robustness evaluation indicators based on network maximum flow: flow capacity robustness, which assesses the ability of the network to resist attack, and flow recovery robustness, which assesses the ability to rebuild the network after an attack on the network. To verify the effectiveness of the robustness indicators proposed in this study, we simulate four typical networks and analyze their robustness, and the results show that a high-density random network is stronger than a low-density network in terms of connectivity and resilience; the growth rate parameter of scale-free network does not have a significant impact on robustness changes in most cases; the greater the average degree of a regular network, the greater the robustness; the robustness of small-world network increases with the increase in the average degree. In addition, there is a critical damage rate (when the node damage rate is less than this critical value, the damaged nodes and edges can almost be completely recovered) when examining flow recovery robustness, and the critical damage rate is around 20%. Flow capacity robustness and flow recovery robustness enrich the network structure indicator system and more comprehensively describe the structural stability of real networks.
Highlights
Nowadays, the network exists in every aspect of human life, and our life is convenient and complicated because of the network
We use the nearest neighbor coupled network (NNC) as the test network; that is, for a given even value of k, the N nodes in the network are connected to a ring, where each node is connected to only k/2 neighboring nodes
We define two types of robustness evaluation indicators based on network maximum flow: the flow capacity robustness, which assesses the ability of the network to resist attack, and the flow recovery robustness, which assesses the ability to rebuild the network after an attack on the network
Summary
The network exists in every aspect of human life, and our life is convenient and complicated because of the network. Whether it is a technical network such as a computer network or a social network such as an interpersonal relationship, it will inevitably be disturbed or damaged, affecting the normal operation of the network, or worse, leading to the paralysis of the network. Network robustness describes the ability of a network to maintain a certain level of structural integrity and original functionality after nodes or edges experience random or deliberate attacks [1]. The early researchers of complex network robustness were Albert et al [3], who pointed out that the Network Robustness Analysis scale-free network is more vulnerable under deliberate attack and more robust when subjected to random attack; Holme et al [4] conducted an in-depth study on the robustness of the network as reflected by the changes in various indicators under different types of attack; Paul et al [5] discussed how to effectively improve network robustness; He C-Q et al [6] summarized the changing trend of robustness under different network topologies; Du W and Cai M et al [7] proposed connection robustness and recovery robustness based on the connectivity and resilience of the network and selected four types of complex networks, including the random network and the scale-free network, for extensive experiments, and it is concluded that the random network is the best robust to deliberate attacks, and the node resilience of the scale-free network is better than the edge; Lu P-L et al [8] explored the impact of the initial clustering coefficient on robustness when attacked by different conditions for three complex networks with the same degree distribution and different clustering coefficients and showed that the larger the initial clustering coefficient, the worse is the robustness of the network
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