Industrial gas–electricity networks typically operate in several modes due to large demand variations. In this article, the nonlinear spatio-temporal transient phenomenon of gas networks (GNs) is analyzed by a novel modeling approach, named Takagi–Sugeno fuzzy linear graph (TSFLG), and then, a parameter space decomposition-based adaptive parameter estimation algorithm is developed for greater efficiency. By merging TS fuzzy theory, the nonlinear terms are replaced by a set of linear elements interpolated by membership functions, which are then connected in series to construct the TSFLG structure. The GN is partitioned into several subnetworks for parallel estimation, and the coupling parameters are determined by the covariance intersection fusion rule. Within each subnetwork, efficiency is further improved by estimating alternately linear and nonlinear parameters. The proposal is assessed in an industrial GN with 12 nodes. Test results indicate that the proposed method improves efficiency by 38.64$\%$ while maintaining accuracy.