In data mining research, outliers usually represent extreme values that deviate from other observations on data. The significant issue of existing outlier detection methods is that they only consider the object itself not taking its neighbouring objects into account to extract location features. In this paper, we propose an innovative approach to this issue. First, we propose the notions of centrality and centre-proximity for determining the degree of outlierness considering the distribution of all objects. We also propose a novel graph-based algorithm for outlier detection based on the notions. The algorithm solves the problems of existing methods, i.e. the problems of local density, micro-cluster, and fringe objects. We performed extensive experiments in order to confirm the effectiveness and efficiency of our proposed method. The obtained experimental results showed that the proposed method uncovers outliers successfully, and outperforms previous outlier detection methods.