Summary: Given interacting entities (customers buying products; Twitter users re-tweeting posts; patients visiting doctors; machines sending packets to machines), how can we spot anomalies and possibly fraud? What should we do if we know that some entities are fraudulent? The problem has attracted huge interest; several suspicious patterns have been discovered, and several tools to spot such patterns have been developed. We survey the most successful, time-tested tools, starting with classic ones (matrix factorization, belief propagation, dense block detection) and continuing with newer, equally successful ones, and specifically multi-relational learning, and graph neural networks GNNs. Focusing on practitioners, we also present some past success stories from diverse settings (phonecall networks, online retailers, social networks); we list some types of fraud and their tell-tale signs; and we also list the node-features that we found most useful (degree, core-number, etc), as well as some graph-visualization tools.

Christos Faloutsos is a Professor at Carnegie Mellon University. He has received the Presidential Young Investigator Award by the National Science Foundation (1989), the Research Contributions Award in ICDM 2006, the SIGKDD Innovations Award (2010), the PAKDD Distinguished Contributions Award (2018), 31 “best paper” awards (including 8 “test of time” awards). He has given over 50 tutorials and over 25 invited distinguished lectures. His research interests include large-scale data mining with emphasis on graphs and time sequences; anomaly detection, tensors, and fractals.

Pedro Fidalgo is the Engineering Director of Risk Management for R&D at Mobileum. He has a Msc in Computer Science from the University of Liverpool, UK and he is a PhD candidate in Complexity Sciences from (ISCTE-IUL), Portugal. His research interests include large-scale data mining with graphs, telecom fraud, anomaly detection and telecom signalling protocols.

Mirela Cazzolato is a Postdoc Fellow in Computer Science at the Institute of Mathematics and Computer Science of the University of São Paulo (ICMC-USP) and the Heart Institute (InCor-USP), Brazil. She spent a year as a visiting researcher at Carnegie Mellon University (CMU), USA. She has a Ph.D. in Computer Science from ICMC-USP, with an internship period abroad at the Karlsruhe Institute of Technology (KIT), Germany. Her research interests include image analysis, graph mining, visualization, content-based retrieval, moving objects, and mHealth.