The multiple relationships among objects in complex systems can be described well by multiplex networks, which contain rich information of the connections between objects. The null model of networks, which can be used to quantify the specific nature of a network, is a powerful tool for analysing the structural characteristics of complex systems. However, the null model for multiplex networks remains largely unexplored. In this paper, we propose a null model for multiplex networks based on the node redundancy degree, which is a natural measure for describing the multiple relationships in multiplex networks. Based on this model, we define the modularity of multiplex networks to study the community structures in multiplex networks and demonstrate our theory in practice through community detection in four real-world networks. The results show that our model can reveal the community structures in multiplex networks and indicate that our null model is a useful approach for providing new insights into the specific nature of multiplex networks, which are difficult to quantify.

No abstract

Network topology measurement is an important component in network research. Network tomography is able to accurately infer network topology by using end-to-end measurement without cooperation of internal routers. Unfortunately, traditional network tomography methods can not accurately estimate topology in the non-stationary network due to the variability of traffic distribution. In this paper, we present a novel network topology inference method based on subset structure fusion for accurate topology inference in the non-stationary network. First, we propose an end-to-end measurement method named threepacket to accurately probe the three-leaf-nodes subset structures of the network without the assumption that the packet delay or loss follows a stable distribution. Second, we propose a metric for the shared path length based on the structural characteristics of the subset structures to fuse these subset structures into a correct complete topology. The analytical and simulation results show that our method is more applicable for topology inference in the non-stationary network compared with the existing methods. INDEX TERMS End-to-end measurement,network tomography,non-stationary network,subset structure fusion,topology inference.

Network topology is important information for many network control and management applications. Network tomography infers network topology from end-to-end measured packet delays or losses, which is more feasible than internal cooperation-based methods and attracts many studies. Most of the existing methods for network topology inference usually function under the assumption that the distribution of packet delay or loss follows a given distribution (e.g., Gaussian or Gaussian mixture), and they estimate network topology from the parameters of the given distribution. However, these methods may fail to obtain an accurate estimation because the real distribution of packet delay or loss usually cannot be described by a certain distribution. In this paper, we present a novel network topology inference method based on the unicast end-to-end measured delays. The method abandons the assumption of packet delay distribution and constructs network topology by inferring the higher-order cumulants of internal links from the end-to-end measured delays. The analytical and simulation results show that the proposed method offers over 10% improvement in accuracy compared with that of the state-of-the-art works. INDEX TERMS Higher-order cumulant, topology inference, end-to-end measurement, network tomography.

Understanding the network link loss is particularly important for optimising delay-sensitive applications. This study addresses the issue of estimating temporal dependence characteristic of link loss by using network tomography. Different from existing works of network loss tomography, the authors use a kth order Markov Chain (k-MC for short, k . 1) to model the packet loss process, and propose a constrained optimisation-based method to estimate the state transmission probabilities of the k-MC link loss model. The authors also propose a top -down algorithm in order to ensure that our method can be applied to large networks. Compared with existing loss tomography methods, our method is capable of obtaining more accurate packet loss probability estimates. The ns-2 simulation results show the good performance of our method.