Research On Hyperbolic Mapping Based Complex Network Survivability Index

Network security situation has become increasingly severe in the network era. The research of network survival technology are very crucial, because that the traditional network security technologies are more and more hardly to deal with the complex and volatile network environment. The complex network theory based on network topology provide a powerful means to the network survival technology. And that hyperbolic geometry of complex network provide a new perspective to the research of structural feature of network topology. Further, this paper use hyperbolic geometry of complex network to research the network topology structure to detect the nodes and links that have huge influence for Network Survivability. At first, this paper proposes three network hyperbolic mapping methods with different precision and speed to map the real networks to hyperbolic space. Then this paper proposes an index to measure the importance of nodes and links based on hyperbolic space, respectively.The existing hyperbolic mapping methods map the nodes one-by-one to the hyperbolic space by maximum likelihood estimation(MLE), which can’t fully utilize the node information, and finally leads to deficiency on algorithm precision and efficiency. Hence, a novel mapping method called Community and Hyperbolic Mapping(CHM) is proposed based on community information in this paper. Firstly, an index called Community Intimacy(CI) is presented to measure the relationship between the communities, based on which a community ordering algorithm is introduced. According to a proposed hypothesis called Community-Sector, which supposes that most nodes of one community gather in the same sector in the hyperbolic space, CHM maps the ordered communities into the hyperbolic space, and then initializes the angular coordinates of the nodes which are very close to their real values in the sector. Therefore, the initialized angular coordinates can be optimized by MLE and using the information of all nodes, which can greatly improve the algorithm precision. Then, based on the phenomenon of the initialized coordinates that the impact between the nodes decrease sharply when increasing the path length, a modified model called Local Community and Hyperbolic Mapping(LCHM) is presented based on the local path information of the nodes, which leads to the time complexity descending to O(n2). Furthermore, the hyperbolic mapping model HCHM is also proposed to reduce the time complexity to near-linear in sparse networks. HCHM uses the hierarchical structure of communities to narrow the possible of angle range by initializing the communities of every levels. The experiments show that CHM and LCHM outperform the existing methods. And although the precision of HCHM is lower than the existing methods, the mapping speed of HCHM outclasses them.Then, this paper researches the issues of the importance of nodes and links by using the networks information under hyperbolic space, respectively. This paper analyzes the relationship among nodes by the coordinate of nodes, and considers the network position of nodes and connectivity of nodes. And then an index called Hyperbolic Centrality is proposed to measure the importance of nodes. Based on the thought of exceptional link of link prediction, and the analysis of the relationship of nodes, this paper proposes an index called Hyperbolic Anomalism to measure the importance of links. The experiments show that the measurement capability of Hyperbolic Centrality and Hyperbolic Anomalism, respectively.