A new method optimizing the subgraph centrality of large networks

Since many realistic networks such as wireless sensor/ad hoc networks usually do not agree very well with the basic network models such as small-word and scale-free models, we often need to obtain some expected structural features such as a small average path length and a regular degree distribution while optimizing the connectivity of these networks. Although a minor addition of links for optimizing network connectivity is not likely to change the structural properties of a network, it is necessary to investigate the impact of link addition on network properties as the number of the added links increases. However, to the best of our knowledge, the study of that problem has not been found so far. Furthermore, two closely related questions to that problem, i.e., how to measure and how to improve network connectivity, have not been studied carefully enough yet. To address the three problems above, the authors derive a better measure of network connectivity for large networks and a new strategy that can increase/decrease network connectivity the most, and propose a spectral density algorithm optimizing the connectivity of large networks, which is able to indicate the impact on the structural properties of a network while increasing/decreasing its connectivity, providing us a guided optimization of network connectivity. In other words, our algorithm can optimize not only the connectivity of a large network but also its structural features. Meanwhile, our new findings about spectral density are also concluded in this paper. In addition, we may also apply this algorithm to solve all eigenvalues of an N×N matrix, with a low complexity of O(N2) at most.