The Braiding Index (BI), defined as the average count of intercepted channels per cross-section, is a widely used metric for characterizing multi-thread river systems. However, it does not account for the diversity of channels (e.g., in terms of discharge) within different cross-sections, omitting important information related to system complexity. Here we present a modification of BI (the Entropic Braiding Index, eBI) which augments the information content in BI by using Shannon Entropy to encode the diversity of channels in each cross section. eBI is interpreted as the number of “effective channels” per cross-section, allowing a direct comparison with the traditional BI. We demonstrate the superior capabilities of eBI via analysis of synthetic, numerical and field examples. In addition, we show that interrogating cross-sections via the ratio BI/eBI has the potential to quantify channel disparity, differentiate types of multi-thread systems, and inform about cross-section stability to forcing variability (e.g., seasonal flooding).