Robustness of complex networks is an essential subject for improving their performance when vertices or links are removed due to potential threats. In recent years, significant advancements have been achieved in this field by many researchers. In this paper we show an overview from a novel statistic perspective. We present a brief review about complex networks at first including 2 primary network models, 12 popular attack strategies and the most convincing network robustness metrics. Then, we focus on the correlations of 12 attack strategies with each other, and the difference of the correlations from one network model to the other. We are also curious about the robustness of networks when vertices are removed according to different attack strategies and the difference of robustness from one network model to the other. Our aim is to observe the correlation mechanism of centralities for distinct network models, and compare the network robustness when different centralities are applied as attacking directors to distinct network models. What inspires us is that maybe we can find a paradigm that combines several high-destructive attack strategies to find the optimal strategy based on the deep learning framework.

The growth of the size of the routing tables limits the scalability of the conventional IP routing. As scalable routing schemes for large-scale networks are highly demanded, this paper proposes and evaluates an efficient geometric routing scheme and related low-cost node design applicable to large-scale networks. The approach guarantees that greedy forwarding on derived coordinates will result in successful packet delivery to every destination in the network by relying on coordinates deduced from a spanning tree of the network. The efficiency of the proposed scheme is measured in terms of routing quality (stretch) and size of the coordinates. The cost of the proposed router is quantified in terms of area complexity of the hardware design and all the evaluations involve comparison with a state-of-the-art approach with virtual coordinates in the hyperbolic plane. Extensive simulations assess the proposal in large topologies consisting of up to 100K nodes. Experiments show that the scheme has stretch properties comparable to geometric routing in the hyperbolic plane, while enabling a more efficient hardware design, and scaling considerably better in terms of storage requirements for coordinate representation. These attractive properties make the scheme promising for routing in large networks.

The link structure of the Web is generally viewed as a webgraph. One of the main objectives of web structure mining is to find hidden communities on the Web based on the webgraph, and one of its approaches tries to enumerate substructures, each of which corresponds to a set of web pages of a community or its core. Research has shown that certain substructures can find sets of pages that are inherently irrelevant to communities. In this paper, we propose a model, which we call contracted webgraphs, where such substructures are contracted into single nodes to hide useless information. We then try structure mining iteratively on those contracted webgraphs since we can expect to find further hidden information once irrelevant information is eliminated. We also explore the structural properties of contracted webgraphs from the viewpoint of scale-freeness, and we observe that they exhibit novel and extreme self-similarities.

For realistic scale-free networks, we investigate the traffic properties of stochastic routing inspired by a zero-range process known in statistical physics. By parameters α and δ, this model controls degree-dependent hopping of packets and forwarding of packets with higher performance at more busy nodes. Through a theoretical analysis and numerical simulations, we derive the condition for the concentration of packets at a few hubs. In particular, we show that the optimal α and δ are involved in the trade-off between a detour path for α < 0 and long wait at hubs for α > 0; In the low-performance regime at a small δ, the wandering path for α < 0 better reduces the mean travel time of a packet with high reachability. Although, in the high-performance regime at a large δ, the difference between α > 0 and α < 0 is small, neither the wandering long path with short wait trapped at nodes (α = -1), nor the short hopping path with long wait trapped at hubs (α = 1) is advisable. A uniformly random walk (α = 0) yields slightly better performance. We also discuss the congestion phenomena in a more complicated situation with packet generation at each time step.

Recent studies investigating the Internet topology reported that inter Autonomous System (AS) topology exhibits a power-law degree distribution which is known as the scale-free property. Although there are many models to generate scale-free topologies, no game theoretic approaches have been proposed yet. In this paper, we propose the new dynamic game theoretic model for the AS level Internet topology formation. Through numerical simulations, we show our process tends to give emergence of the topologies which have the scale-free property especially in the case of large decay parameters and large random link costs. The significance of our study is summarized as following three topics. Firstly, we show that scale-free topologies can also emerge from the game theoretic model. Secondly, we propose the new dynamic process of the network formation game for modeling a process of AS topology formation, and show that our model is appropriate in the micro and macro senses. In the micro sense, our topology formation process is appropriate because this represents competitive and distributed situation observed in the real AS level Internet topology formation process. In the macro sense, some of statistical properties of emergent topologies from our process are similar to those of which also observed in the real AS level Internet topology. Finally, we demonstrate the numerical simulations of our process which is deterministic variation of dynamic process of network formation game with transfers. This is also the new result in the field of the game theory.

The number of customers of a service for Internet access from cellular phones in Japan has been explosively increasing for some time. We analyze the relation between the number of customers and the volume of traffic, with a view to finding clues to the structure of human relations among the very large set of potential customers of the service. The traffic data reveals that this structure is a scale-free network, and we calculate the exponent that governs the distribution of node degree in this network. The data also indicates that people who have many friends tend to subscribe to the service at an earlier stage. These results are useful for investigating various fields, including marketing strategies, the propagation of rumors, the spread of computer viruses, and so on.