Given a heterogeneous multilayer network with various connections in pharmacology, how can we detect components with intensive interactions and strong dependencies? Can we accurately capture suspicious groups in a multi-lot transaction network under camouflage? These challenges related to dense subgraph detection have been extensively studied in simple graphs but remain under-explored in complex networks. Existing methods struggle to effectively handle the intricate dependencies, let alone accurately identify the interrelated dense connected patterns within a series of complex heterogeneous networks. Here, we introduce INDUEN, a novel algorithm designed to detect interrelated densest subgraphs in multilayer networks by leveraging joint optimization of coupled factorization and local search for an elaborate-designed joint density measure. Experimental results demonstrate that INDUEN outperforms the state-of-the-art baselines in accurately detecting interrelated densest sub graphs under various settings. Furthermore, INDUEN uncovers some intriguing patterns in real-world data; it is linearly scalable and achieves more than 35 × speedup compared to the state-of-the-art method Destine.

Given a heterogeneous multilayer network with various connections in pharmacology, how can we detect components with intensive interactions and strong dependencies? Can we accurately capture suspicious groups in a multi-lot transaction network under camouflage? These challenges related to dense subgraph detection have been extensively studied in simple graphs (such as bipartite graph, multi-view network) but remain under-explored on complex networks. Existing methods struggle to effectively handle theintricate dependencies, let alone accurately identify theinterrelated dense connected patternswithin a series of complex heterogeneous networks. In this paper, we proposeInDuen, a novel algorithm designed to detect interrelated densest subgraphs in multilayer networks through joint optimization of coupled factorization and local search for an elaborate-designed joint density measure. It is(a)effective for both large synthetic and real networks,(b)resistant to camouflage for anomaly detection, and(c)linearly scalable. Experimental results demonstrate thatInDuenoutperforms the state-of-the-art baselines in accurately detecting interrelated densest subgraphs under various settings. Furthermore,InDuenuncovers some intriguing patterns in real-world data, i.e., closely cooperated academic groups and interrelated dependent functional components in biology-net.InDuenachieves more than$35 \times$speedup compared to the SOTA methodDestine.