The lack of regulation and the ease with which funds can be transferred across networks raise the cross-chain security issues. Since 2020, criminals have laundered at least $4 billion worth of illicit crypto proceeds using cross-chain technologies (Elliptic, The state of cross-chain crime. Tech. rep. (2022). https://www.elliptic.co/hubfs/Cross%20Chain%20Report%20exec.pdf ). In fact, above security issues, even criminals can be identified from abnormal account activities. Abnormal account activity refers to transactions that deviate from expected patterns or suspicious characteristics, potentially indicating fraudulent or malicious behavior. To identify abnormal transactions, there are mainly two types of solutions, i.e., machine learning algorithms (Chen et al., Secur Commun Networks 2021:6643763:1–6643763:10, 2021a; Hu et al., BERT4ETH: A pre-trained transformer for ethereum fraud detection. In: Ding Y, Tang J, Sequeda JF, Aroyo L, Castillo C, Houben G (eds) WWW 2023, ACM, pp 2189–2197 (2023); Wu et al., IEEE Trans Syst Man Cybern Syst 52(2):1156–1166, 2022) and graph-based approaches (Chen et al., Phishing scam detection on ethereum: Towards financial security for blockchain ecosystem. In: Bessiere C (ed) IJCAI 2020, ijcai.org, pp 4506–4512 (2020); Yu et al., Abnormal transaction detection based on graph networks. In: COMPSAC 2021, IEEE, pp 312–317 (2021)). Machine learning algorithms use statistical techniques to identify patterns and relationships within datasets, allowing the system to generalize and make predictions on unseen data. Graph-based approaches leverage graph structures to represent and analyze relationships and connections between entities. Previous research in abnormal account detection has predominantly focused on applying these techniques to single-chain networks (Li et al., TTAGN: temporal transaction aggregation graph network for ethereum phishing scams detection. In: Laforest F, Troncy R, Simperl E, Agarwal D, Gionis A, Herman I, Médini L (eds) WWW ’22, ACM, pp 661–669 (2022a); Zhang et al., J Syst Archit 110:101829, 2020), such as the Bitcoin blockchain and Ethereum. However, applying these techniques directly to cross-chain transactions poses unique challenges, which can be described as follows.