JECHO: Scalable Echo Chamber Detection via Jaccard-based Homophily and Seed Expansion

Detecting echo chambers is critical for understanding and limiting negative social phenomena, such as online polarization, misinformation, and conspiracy theory diffusion. However, the echo chamber detection (ECD) problem yet lacks a rigorous algorithmic foundation. We address this gap by formalizing a unified definition of echo chambers based on three principles: internal opinion homogeneity, opinion extremism, and structural isolation. Under such a definition, we establish the theoretical hardness of the ECD problem, proving it is NP-hard via a reduction from the conductance minimization problem. To circumvent this computational barrier, we derive a theoretical lower bound on the Jaccard-based homophily (JHO) of nodes that reside within valid echo chambers. This guarantee motivates JECHO, a novel algorithm that detects echo chambers via local seed expansion rather than global enumeration. JECHO first identifies seeds that exceed the JHO threshold and then applies a score-based expansion to optimize structural isolation. Extensive experiments on real-world and synthetic networks demonstrate that our theory-guided approach detects more structurally isolated echo chambers than state-of-the-art methods while reducing runtime by orders of magnitude.