Ground family education explanation based on visibility graph of complex network by temporal community division

Introduction Family education directly shapes adolescents’ positive behavioral habits, moral character, and cultural refinement, making it a critical component of their healthy development. With AI technology evolving at such a fast pace, search engines and social media platforms constantly generate vast amounts of data. Analyzing these data provides a quick understanding of the public’s attention to family education and how the characteristics of that attention have evolved over time, and this is critical for policy intervention and decision-making in family education. Methods The visibility graph (VG) has proven effective for nonlinear time series analysis in a range of real-world settings. Given the significant temporal fluctuations and nonlinear characteristics of public attention, this study utilized 1,882 daily observations of the comprehensive index for “family education” on Douyin, covering the period from January 1, 2021, to 25 February 2026, and mapped these data onto a natural visibility graph comprising 1,882 nodes and 3,738 edges, in order to examine its underlying complex network metrics. Subsequently, the greedy modularity optimization (Greedy Modularity Optimisation) algorithm was employed to resolve the internal community structure of the network. Finally, the evolutionary trend of public attention to family education over time was elucidated by combining the temporal features of each community with their cross-seasonal variation patterns. Meanwhile, to mitigate potential methodological limitation, the above descriptive findings were further subjected to formal statistical testing and robustness analyses: first, confirmatory maximum-likelihood analysis of the degree distribution was conducted; second, a null-model comparisons were performed; third, bootstrap confidence intervals were estimated and a modularity permutation test was carried out; fourth, sensitivity of community-detection algorithms and resolution-parameters was assessed; and fifth, a parallel analysis of the Search Index was performed. Results The family education composite network exhibits significant non-random structural properties: its degree distribution follows a heavy-tailed form (with a finite-size cutoff rather than a pure power law), alongside small-world clustering and a remarkably high modularity index (Q > 0.9066). These findings are robustly supported by confirmatory maximum likelihood estimation, Kolmogorov-Smirnov tests, and multiple sensitivity analyses. Notably, the network’s community dynamics display clear temporal rhythms, correlating not only with the academic year cycle, the phased implementation of the “Double Reduction” policy, and the enactment of the Preschool Education Law, but also with seasonal patterns (permutation test p = 0.0001; Cramér’s V = 0.591). This temporal structure is further corroborated by a parallel search index analysis, strengthening the credibility of our conclusions. Discussion These findings suggest that the visibility graph method is a practical and feasible approach for analyzing public attention. Combined with community detection, this study reveals the structural features and temporal evolution patterns of public attention to this issue. A single-layer Natural Visibility Graph (NVG) framework suffices to extract meaningful community structures from social search time series without requiring multi-layer aggregation, and this to some extent addresses the limitations of existing research methods.