Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured {\em graph} data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we provide a comprehensive exploration of both data mining and machine learning algorithms for these {\em detection} tasks. we give a general framework for the algorithms categorized under various settings: unsupervised vs. (semi-)supervised approaches, for static vs. dynamic graphs, for attributed vs. plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly {\em attribution} and highlight the major techniques that facilitate digging out the root cause, or the `why', of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field.

The problem of anomaly detection has been studied for a long time. In short, anomalies are abnormal or unlikely things. In financial networks, thieves and illegal activities are often anomalous in nature. Members of a network want to detect anomalies as soon as possible to prevent them from harming the network's community and integrity. Many Machine Learning techniques have been proposed to deal with this problem; some results appear to be quite promising but there is no obvious superior method. In this paper, we consider anomaly detection particular to the Bitcoin transaction network. Our goal is to detect which users and transactions are the most suspicious; in this case, anomalous behavior is a proxy for suspicious behavior. To this end, we use three unsupervised learning methods including k-means clustering, Mahalanobis distance, and Unsupervised Support Vector Machine (SVM) on two graphs generated by the Bitcoin transaction network: one graph has users as nodes, and the other has transactions as nodes.