Outlier detection algorithms are widely used in various fields such as network intrusion detection, and medical aided diagnosis. Local Distance-Based Outlier Factor (LDOF), Cohesiveness-Based Outlier Factor (CBOF) and Local Outlier Factor (LOF) algorithms are classic algorithms for outlier detection with long execution time and low detection rate on large-scale datasets and high dimensional datasets. Aiming at these problems, an outlier detection algorithm Based on Graph Random Walk (BGRW) was proposed. Firstly, the iterations, damping factor and outlier degree for every object in the dataset were initialized. Then, the transition probability of the rambler between objects was deduced based on the Euclidean distance between the objects. And the outlier degree of every object in the dataset was calculated by iteration. Finally, the objects with highest outlier degree were output as outliers. On UCI （University of California， Irvine） real datasets and synthetic datasets with complex distribution, comparison between BGRW and LDOF, CBOF, LOF algorithms about detection rate, execution time and false positive rate were carried out. The experimental results show that BGRW is able to decrease execution time and false positive rate, and has higher detection rate.

Enhancing the accuracy of link prediction is one of the fundamental problems in the research of complex networks. The existing node similarity-based prediction indexes do not make full use of the importance influences of the nodes in the network. In order to solve the above problem, a link prediction algorithm based on the node importance was proposed. The node degree centrality, closeness centrality and betweenness centrality were used on the basis of similarity indexes such as Common Neighbor (CN), Adamic-Adar (AA) and Resource Allocation (RA) of local similarity-based link prediction algorithm. The link prediction indexes of CN, AA and RA with considering the importance of nodes were proposed to calculate the node similarity. The simulation experiments were taken on four real-world networks and Area Under the receiver operation characteristic Curve (AUC) was adopted as the standard index of link prediction accuracy. The experimental results show that the link prediction accuracies of the proposed algorithm on four data sets are higher than those of the other comparison algorithms, like Common Neighbor (CN) and so on. The proposed algorithm outperforms traditional link prediction algorithm and produces more accurate prediction on the complex network.