An optimization-based algorithm for obtaining an optimal synchronizable network after link addition or reduction

Achieving a network structure with optimal synchronization is essential in many applications. This paper proposes an optimization algorithm for constructing a network with optimal synchronization. The introduced algorithm is based on the eigenvalues of the connectivity matrix. The performance of the proposed algorithm is compared with random link addition and a method based on the eigenvector centrality. It is shown that the proposed algorithm has a better synchronization ability than the other methods and also the scale-free and small-world networks with the same number of nodes and links. The proposed algorithm can also be applied for link reduction while less disturbing its synchronization. The effectiveness of the algorithm is compared with four other link reduction methods. The results represent that the proposed algorithm is the most appropriate method for preserving synchronization.

The Statistical Analysis of Top Hubs in Growing Geographical Networks with Optimal Policy

Many practical networks, such as city networks, road networks and neural networks, usually grow up on basis of topological structures and geographical measures. Big hubs, importance of which have been well known in complex networks, still play crucial roles in growing networks with geographical measures. Therefore, it is very necessary to investigate the underlying mechanisms of statistical features of different top hubs in such networks. Here, we propose a growing network model based on optimal policy in geographical ground. Through the statistics of a great number of geographical networks, we find that the degree and position distributions of top four hubs are diverse between them and closely interrelated with each other, and further gain the relationships between the upper limits of top hubs and the size of networks. Then, the underlying mechanisms are explored. Meanwhile, we are diligent to obtain the corresponding relationships of different spatial distribution areas for different top hubs, and compute their abnormal average degrees at different spatial positions, which show significant differences and imply the advantage of spatial positions and intense competition between top hubs. We hope our results could offer useful inspirations for related practical network studies.

A new method to reduce the number of time delays in a network

Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can have unexpected behaviours when the signal between the vertices are time delayed. It has been shown for a very general class of systems that the time delays can be rearranged as long as the total time delay over the constitutive loops of the network is conserved. This fact allows to reduce the number of time delays of the problem without loss of information. There is a theoretical lower bound for this number that can be numerically improved if the time delays are commensurable. Here we propose a formulation of the problem and a numerical method to even further reduce the number of time delays in a network.

Role of structural holes in containing spreading processes

Structural holes are channels or paths spanned by a group of indirectly connected nodes and their intermediary in a network. In this work we emphasize the interesting role of structural holes as brokers for information propagation. Based on the distribution of the structural hole numbers associated with each node, we propose a simple yet effective approach for choosing the most influential nodes to immunize in containing the spreading processes. Using a wide spectrum of large real-world networks, we demonstrate that the proposed approach outperforms conventional methods in a remarkable way. In particular, we find that the performance gains of our approach are particularly prominent for networks with high transitivity and assortativity, which verifies the vital role of structural holes in information diffusion on networked systems.