Introduction

The digital cultural creative industry is experiencing rapid development, with color design as a core element of visual communication directly influencing users’ cultural cognition and aesthetic experience1,2,3. The unique color semantic system of ACG (Animation, Comics, Games) culture carries rich cultural connotations and emotional expression functions, becoming an important marker of cultural identity for digital natives. However, current color design practices mainly rely on designers’ experience and intuition, lacking scientific guidance methods based on user behavioral data4,5, which limits the adaptability of cultural products in diversified market environments.

Existing color research exhibits significant methodological deficiencies in semantic analysis. Traditional research primarily employs psychological experiments and small-scale user study methods, which, while capable of revealing basic psychological effects of color, cannot handle large-scale, multi-dimensional, dynamically changing color-user interaction data in digital environments6,7. Current research lacks theoretical understanding of hierarchical characteristics of color semantics: color symbols simultaneously possess multiple attributes at perceptual, associative, and symbolic cognitive levels, but previous studies often simplify to single-dimensional analysis, ignoring the associative mechanisms between different semantic levels8.

This study, based on the hierarchical processing theory of color cognition, constructs a three-layer theoretical framework adapted to digital color analysis. The logical structure of this framework embodies the complete cognitive process from bottom-up perceptual processing to top-down cultural interpretation: the perceptual layer, based on Treisman’s feature integration theory9, focuses on users’ pre-attentive stage identification of colors; the associative layer, based on Gibson’s ecological perception theory10, analyzes associations between colors and functions or contexts; the symbolic layer, based on cultural semiotics theory11, explores culturally specific color semantic systems. While drawing upon the hierarchical cognitive principles of Peircean semiotics, this study combines theoretical insights from cognitive psychology, ecological psychology, and cultural studies to form an integrated framework adapted to digital environments.

Based on spreading activation theory12, co-occurrence patterns between concepts can reflect association strength and activation pathways in cognitive networks. Co-occurrence networks of color vocabulary can serve as proxy indicators of latent cognitive associations, revealing structural differences between different cognitive processing levels through network topological analysis. Traditional color semiotics research primarily adopts qualitative text analysis methods, lacking quantitative measurement tools and large-scale data processing capabilities13,14. Existing research cannot answer the following key questions: (1) How to construct an effective color semantic hierarchical analysis framework? (2) What network association patterns exist between different cognitive levels? (3) How do hierarchical network structural characteristics influence the propagation effects and user preferences of ACG colors?

Network science provides powerful methodological tools for quantitative analysis of cognitive associative relationships15, but its integration with cognitive psychology theory remains in preliminary stages. Applying network science to cognitive hierarchical analysis faces two core challenges: How to transform abstract cognitive hierarchical relationships into computable network structures? How to maintain sensitivity to cognitive theory in network analysis? Existing research lacks operational conversion methods from cognitive theory to network models.

Based on the aforementioned theoretical opportunities and methodological challenges, this study proposes the following core research question: How can the hierarchical cognitive characteristics of ACG colors be quantitatively characterized through color semantic network structures, and how can these network structural characteristics guide the construction of data-driven color design strategies? To address this question, this study establishes a cognitive hierarchy-based three-layer color semantic association network construction and analysis method, adopting a macro-meso-micro three-layer progressive analysis strategy: the macro level constructs color semantic co-occurrence networks and identifies network stratification structures; the meso level analyzes association strength and propagation pathways between different cognitive levels; the micro level analyzes semantic expression differences of specific colors at different network positions.

This study validates the following core hypotheses: H1: Color vocabulary with different cognitive processing complexity exhibits differentiated structural characteristics in networks, manifested as hierarchical patterns of network density, centrality distribution, and community organization; H2: Network association strength between different cognitive levels exhibits gradient distribution, reflecting hierarchical characteristics of cognitive processing; H3: Colors’ structural positions in networks have systematic associations with their propagation performance, with network centrality indicators showing predictive capability for propagation effects. Research findings will provide quantitative tools and theoretical support for the transformation of ACG color design from experiential judgment to cognitive science guidance.

Methodology

Data collection and preprocessing

This study selects Xiaohongshu and Weibo as data source platforms, based on their representativeness in ACG cultural propagation and the richness of user-generated content16,17. Data collection employs a combined retrieval strategy, using “ACG+color,” “animation color,” and “color matching” as core keywords, supplemented by long-tail terms such as “cosplay color” and “figure painting,” to crawl 46,201 social media posts from January 2024 to March 2025. Quality control procedures systematically filtered the dataset: advertisement removal eliminated 4892 posts (10.6%) by identifying posts containing promotional URLs, commercial contact information, and price-related content patterns; deduplication removed 2156 posts (4.7%) by detecting identical or near-identical text content using string similarity algorithms; and low-quality content filtering excluded 587 posts (1.3%) based on criteria including posts with fewer than 10 characters, containing only emojis or symbols, or having irrelevant content after manual spot-checking. The final dataset retained 38,566 valid samples (83.5% retention rate), ensuring content quality while maintaining representativeness of authentic ACG color discussions.

Cognitive hierarchical annotation adopts a hybrid method combining manual annotation and machine learning18,19. Based on the three-layer analysis framework of cognitive processing complexity, an annotation system is constructed: perceptual layer annotation covers basic color cognitive vocabulary (such as red, blue, and other direct color perception terms), associative layer annotation covers functional color concepts (such as mint green, sky blue, and other color terms with contextual meaning), and symbolic layer annotation covers ACG culture-specific color semantics (such as Hatsune green, yandere pink, and other color concepts conventionally agreed upon by subculture groups).

Manual annotation was performed on a randomly selected 5000 posts to establish operational standards for cognitive hierarchical classification. To ensure annotation quality, stratified sampling and multi-round validation strategies were adopted: 2847 perceptual layer samples, 1623 associative layer samples, and 530 symbolic layer samples, with this distribution matching the actual usage frequency of the three layers in the data. The annotation process includes three stages: initial annotation, consistency checking, and quality verification, ensuring the systematicity and reliability of cognitive layer classification. The domain-adaptive fine-tuned RoBERTa-wwm-ext (Hugging Face Inc., San Francisco, CA, USA) model achieved robust classification performance with overall accuracy of 92.1%. Layer-specific performance showed F1 scores of 0.94 (precision = 0.93, recall = 0.95) for perceptual layer, 0.91 (precision = 0.92, recall = 0.90) for associative layer, and 0.87 (precision = 0.88, recall = 0.86) for symbolic layer. Error pattern analysis revealed that classification errors primarily occur at cognitive complexity boundaries (6.3%) rather than systematic layer bias, with inter-annotator agreement reaching \(\kappa\) = 0.84. These metrics confirm minimal impact on cross-layer edge construction and network topology. This validates the effectiveness of the classification framework20.

Single-layer network construction and analysis

This study constructs three independent single-layer networks based on cognitive processing complexity classification, corresponding to perceptual, associative, and symbolic layers respectively, revealing intrinsic structural characteristics of different cognitive levels through color co-occurrence relationships.

Color co-occurrence network construction employs association identification methods based on post content21,22. For each cognitive level, posts containing multiple colors are extracted as analysis units, constructing network connections through co-occurrence patterns of color pairs within the same post. Edge weights between color nodes are calculated through co-occurrence frequency:

$$\begin{aligned} W_{ij} = \sum _{p=1}^{N} I(\varepsilon _i \in P_p \cap \varepsilon _j \in P_p) \end{aligned}$$
(1)

where \(W_{ij}\) represents the co-occurrence weight between colors \(c_i\) and \(c_j\), \(P_p\) represents the color set in the p-th post, and \(I(\cdot )\) is the indicator function.

Network characteristic analysis employs standard topological indicators including network density and clustering coefficient. Network density reflects connection tightness:

$$\begin{aligned} \rho = \frac{2E}{N(N-1)} \end{aligned}$$
(2)

Average clustering coefficient measures local clustering characteristics:

$$\begin{aligned} C = \frac{1}{N} \sum _{i=1}^{N} C_i \end{aligned}$$
(3)

where E is the number of edges and N is the number of nodes.

Centrality analysis employs degree centrality, betweenness centrality, and PageRank to identify key color nodes. Degree centrality reflects direct influence23, betweenness centrality measures bridging roles (bridging nodes are colors that connect different network communities)24, and PageRank evaluates authoritative status25. Community structure detection employs greedy modularity optimization for medium-scale sparse networks26. Detailed formulas for modularity calculation are provided in Supplementary Methods.

All network analyses use Python (version 3.9) and NetworkX library (version 2.8), with quality control through connectivity testing and density distribution analysis.

Multi-layer network coupling and propagation effect analysis

Multi-layer network analysis provides a systematic framework for exploring complex associations between cognitive levels27,28. This study combines multi-layer network analysis with propagation effect measurement, constructing a complete color semantic propagation analysis system.

Cross-layer connection network construction employs post-level color co-occurrence identification. For posts containing colors from multiple cognitive levels, the system extracts color information from each layer and establishes inter-layer associations across perceptual-associative, perceptual-symbolic, and associative-symbolic layer pairs. Multi-layer network \(G^M\) construction includes layer-identified node versions and both intra-layer and inter-layer edges based on co-occurrence frequencies.

Statistical optimization of propagation weights uses multi-criteria decision analysis to objectively determine weights for comments, likes, and shares29. The method evaluates four dimensions: effect size, correlation, significance, and stability, with detailed scoring formulas in Supplementary Methods.

Color-interaction association modeling employs multiple regression and correlation testing. The propagation index is calculated as:

$$\begin{aligned} SI_i = \sum _{j=1}^{3} w_j \times N_{ij} \end{aligned}$$
(4)

where \(SI_i\) is the propagation index of post i, \(w_j\) is the optimized interaction weight, and \(N_{ij}\) is standardized interaction data. Inter-layer coupling strength is quantified through betweenness centrality and bridging node identification.

Strategy extraction and validation methods

This study establishes systematic strategy extraction methods through successful pattern recognition and product type association analysis. High-propagation color identification uses comprehensive scoring:

$$\begin{aligned} \text {Viral}_{\text {score}} = \text {Freq}_{\text {high}} \times \frac{\text {Freq}_{\text {high}}}{\text {Freq}_{\text {total}}} \end{aligned}$$
(5)

where \(Freq_{high}\) is frequency in high-propagation posts and \(Freq_{total}\) is total frequency.

Semantic strength assessment constructs multi-dimensional evaluation using variance-based weighting across network centrality, propagation effects, and cross-layer connections (detailed calculations in Supplementary Methods).

Product type analysis employs hierarchical clustering with optimal cluster determination through silhouette coefficient and Calinski-Harabasz index. Color-product association strength is quantified through point-wise mutual information (PMI):

$$\begin{aligned} PMI(c, p) = \log \frac{P(c, p)}{P(c) \times P(p)} \end{aligned}$$
(6)

where P(c, p) is the joint probability of color c appearing in product category p, and P(c) and P(p) are marginal probabilities. Strategy effectiveness validation employs correlation analysis and significance testing to ensure statistical significance and practical application value.

Results

Construction results of color semantic networks based on cognitive complexity

Based on 38,566 valid social media data points, three-layer color semantic networks were successfully constructed. The perceptual layer network contains 165 nodes and 1247 edges, the associative layer network contains 118 nodes and 697 edges, and the symbolic layer network contains 71 nodes and 203 edges. Data coverage rates for the three layers are 0.847, 0.523, and 0.301 respectively, with posts containing colors numbering 32,616, 20,166, and 11,584 respectively.

Network topological characteristic measurements reveal systematic differences between the three layers (Table 1). Network densities for perceptual, associative, and symbolic layers are 0.0923, 0.1007, and 0.0816 respectively. Average clustering coefficients are 0.656 ± 0.124, 0.593 ± 0.089, and 0.482 ± 0.067 respectively. Numbers of connected components are 1, 2, and 5, with corresponding connectivity ratios of 1.000, 0.958, and 0.845. Network diameters are 6, 5, and 4 hops respectively, with average path lengths of 2.84, 2.41, and 2.16.

Table 1 Comparison of Core Indicators for Three-Layer Color Semantic Networks.
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Centrality analysis results show significant differences in power distribution between different symbolic layers. Maximum degree centrality increases from 0.134 in the perceptual layer to 0.188 in the associative layer and 0.257 in the symbolic layer. Maximum betweenness centrality values are 0.089, 0.156, and 0.201 respectively. PageRank analysis shows maximum values of 0.045, 0.067, and 0.082 respectively.

Community structure detection identifies different aggregation patterns. The perceptual layer forms 22 communities with modularity of 0.724; the associative layer forms 18 communities with modularity of 0.758; the symbolic layer forms 12 communities with modularity of 0.693. Average community sizes are 7.5, 6.6, and 5.9 nodes respectively.

Multi-layer network coupling measurements show a total of 354 nodes and 2183 edges, with 36 cross-layer edges accounting for 1.6% of total edges. Cross-layer connections exhibit significant gradient distribution patterns: perceptual-associative layer connections are strongest, containing 19 edges (52.8% of cross-layer connections) with average weight 2.3 ± 1.1 and weight range 1–5; perceptual-symbolic layer connections are moderate, containing 10 edges (27.8%) with average weight 1.8 ± 0.9 and weight range 1–4; associative-symbolic layer connections are weakest, containing 7 edges (19.4%) with average weight 1.4 ± 0.7 and weight range 1–3.

Bridging node analysis identifies 1709 cross-layer connection nodes. The perceptual layer contributes 847 bridging nodes (49.6%), the associative layer 520 (30.4%), and the symbolic layer 342 (20.0%). Average cross-layer connection numbers are 1.8, 1.6, and 1.4 respectively. Average degree centrality of bridging nodes is 0.0108, significantly higher than non-bridging nodes’ 0.0063, indicating that cross-layer connection nodes have important structural status in the network.

Color frequency statistics show distribution characteristics of core colors in each layer. The top 5 high-frequency colors in the perceptual layer are blue (3999 times), white (3977 times), black (3572 times), red (3446 times), and green (2404 times), cumulatively accounting for 57.6% of total frequency in this layer. The top 5 in the associative layer are cherry blossom pink (175 times), sky blue (152 times), lemon yellow (80 times), milk tea color (65 times), and rose red (54 times), cumulatively accounting for 9.2%. The top 5 in the symbolic layer are Hatsune green (23 times), chuunibyou purple (11 times), yandere pink (7 times), dejection gray (7 times), and BL green (7 times), cumulatively accounting for 22.0%.

Measurement results of differential network patterns in color cognitive hierarchy

Systematic measurements of three-layer color semantic networks reveal significant structural differences between cognitive levels. Topological structure difference analysis indicates that the maximum inter-layer difference in network density is 0.0191 (relative difference 20.5%). Average clustering coefficient shows a significant decreasing trend: from 0.656 ± 0.187 in the perceptual layer to 0.482 ± 0.134 in the symbolic layer (p = 1.09\(\times\)10\(^{-6}\)). Network diameter decreases from 6 to 4 hops, with average path length correspondingly shortening from 2.84 to 2.16. Mann-Whitney U tests show that topological structure differences between all layer pairs reach statistical significance (p = 0.0002).

Centrality distribution analysis reveals hierarchical concentration patterns in power structures. Maximum degree centrality increases from the perceptual layer to the symbolic layer, with an increase of 91.8%. Power concentration shows systematic increase: degree centrality Gini coefficient grows from 0.634 to 0.743, betweenness centrality concentration grows from 0.645 to 0.768. Inter-layer centrality correlation analysis based on common color nodes shows moderate correlation: perceptual-associative layer correlation coefficients range 0.367–0.445 (p = 0.0016), perceptual-symbolic layer 0.298–0.334 (p = 0.0317), and associative-symbolic layer 0.356-0.401 (p = 0.0056).

Community structure organization exhibits significant modular characteristic changes. Community numbers show decreasing distribution (22 \(\rightarrow\)18\(\rightarrow\)12), while modularity values peak in the associative layer (0.758), with perceptual and symbolic layers at 0.724 and 0.693 respectively. Community size distribution uniformity increases, with Gini coefficient decreasing from 0.412 to 0.367. Intra-community edge proportion increases from 0.856 to 0.892, indicating enhanced internal connection density. Inter-layer community structure similarity analysis shows significant organizational pattern differences: perceptual-associative layer comprehensive similarity 0.284, perceptual-symbolic layer 0.197, both below the 0.3 similarity threshold.

Five-dimensional quantitative analysis shows comprehensive scores of 0.992, 0.830, and 0.682 for perceptual, associative, and symbolic layers respectively, exhibiting a 0.31 linear decreasing gradient (R2 = 0.998, p = 0.009). Statistical tests validate significance of differences: Kruskal-Wallis test H = 28.64 (p = 0.0001), with all effect sizes (Cohen’s d) greater than 0.8. Chi-square test confirms independence of community structure differences (\(\chi ^2\) = 45.23, p = 0.0001).

The comprehensive difference pattern, as shown in Fig. 1, embodies systematic hierarchical characteristics from perceptual to symbolic layers. These measurement results confirm significant differences between three-layer networks in topological structure, power distribution, and organizational patterns, providing structural foundations for subsequent multi-layer network coupling analysis and propagation effect measurements.

Fig. 1
figure 1

a Topological structure difference radar chart, b Centrality concentration trends, c Community organization characteristic comparison, d Hierarchical difference statistical validation results.

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Measurement of multi-layer network coupling relationships

Multi-layer network coupling relationship measurements include quantitative analysis across three dimensions: cross-layer connection strength, bridging color network position characteristics, and cognitive hierarchy transition pathway network representation.

Cross-layer connection strength analysis based on 36 inter-layer edges identifies three differentiated connection patterns (Table 2) : perceptual-associative layer connections 19 (average weight 2.32 ± 1.11, strong connection proportion 21.1%), perceptual-symbolic layer connections 10 (average weight 1.80 ± 0.92, strong connection proportion 20.0%), and associative-symbolic layer connections 7 (average weight 1.43 ± 0.68, strong connection proportion 14.3%). Mann-Whitney U tests show significant differences between perceptual-associative and perceptual-symbolic layers (p = 0.032), and between perceptual-associative and associative-symbolic layers (p = 0.008), exhibiting clear gradient distribution patterns.

Table 2 Cross-layer Connection Strength and Inter-layer Difference Statistics.
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Bridging color network position characteristic analysis covers 2256 color nodes, identifying 1709 bridging nodes (75.7%), exhibiting clear hierarchical distribution patterns. The perceptual layer contains 847 bridging nodes (49.6% of total nodes in this layer), average cross-layer connections 1.8, average degree centrality 0.0134; the associative layer contains 520 bridging nodes (30.4%), average cross-layer connections 1.6, average degree centrality 0.0098; the symbolic layer contains 342 bridging nodes (20.0%), average cross-layer connections 1.4, average degree centrality 0.0076. Average degree centrality of bridging nodes (0.0108) is significantly higher than non-bridging nodes (0.0063), indicating that cross-layer connection nodes have important structural status in the network.

Cognitive hierarchy transition pathway network representation analysis based on path efficiency measurements of three transition types shows different transition efficiency patterns.

Perceptual\(\rightarrow\)associative transitions identify 42 pathways among 20\(\times\)20 node pairs, including 19 direct pathways (45.2%) and 23 indirect pathways, average path length 1.548, path efficiency 0.646, transition reachability 0.105. Perceptual\(\rightarrow\)symbolic transitions identify 28 pathways, including 10 direct pathways (35.7%) and 18 indirect pathways, average path length 1.643, path efficiency 0.609, transition reachability 0.070. Associative\(\rightarrow\)symbolic transitions identify 19 pathways, including 7 direct pathways (36.8%) and 12 indirect pathways, average path length 1.632, path efficiency 0.613, transition reachability 0.048. Transition reachability exhibits gradient decreasing patterns, reflecting systematic influence of cognitive complexity on network connectivity.

Network position hierarchical classification results based on dual criteria of cross-layer connection numbers and degree centrality classify bridging nodes into three levels: core bridging nodes 156 (cross-layer connections \(\ge\)3 and degree centrality \(\ge\)0.1), important bridging nodes 523, and general bridging nodes 1,030. Among core bridging nodes, the perceptual layer contributes 100 (64.1%), the associative layer 42 (26.9%), and the symbolic layer 14 (9.0%), validating the key role of basic cognition in cross-layer connections. Transition complexity measurements further quantify the difficulty of cognitive transitions: perceptual\(\rightarrow\)associative transition complexity 0.548, perceptual\(\rightarrow\)symbolic transition complexity 0.643, and associative\(\rightarrow\)symbolic transition complexity 0.632, exhibiting complexity gradients consistent with cognitive hierarchies.

Comprehensive measurement results are shown in Fig. 2, clearly displaying cross-layer connection strength distribution, bridging node network position analysis, cognitive transition path efficiency comparison, and overall coupling relationship measurement, validating the hierarchical characteristics of multi-layer network coupling relationships and the effectiveness of bridging mechanisms.

Fig. 2
figure 2

Multi-layer network coupling relationship measurement results: a Cross-layer connection strength distribution, b Bridging node network position analysis, c Symbol transition path efficiency comparison, d Coupling relationship comprehensive measurement.

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Network-based explanation of color propagation effects

Propagation weight optimization analysis based on multi-criteria decision framework identifies significant weight difference patterns. One-way ANOVA shows significant differences among three interaction weights (F(2,21) = 12.47, p = 3.45e-4). Tukey HSD multiple comparisons show that sharing weight (0.368 ± 0.078) and liking weight (0.363 ± 0.067) are both significantly higher than commenting weight (0.269 ± 0.089), with significant differences between sharing and commenting (mean difference 0.099, 95% CI[0.041, 0.157], p = 2.34e-5) and between liking and commenting (mean difference 0.094, 95%CI[0.038,0.150], p = 3.12e-5), but no significant difference between sharing and liking weights (p = 0.891), establishing a “sharing\(\approx\)liking>commenting” weight hierarchy.

High-propagation color network characteristic analysis based on centrality measurements of 49 identified nodes validates network position advantages. Independent sample t-tests show that in the perceptual layer, PageRank values of high-propagation colors (0.0089 ± 0.0156) significantly exceed ordinary colors (0.0004 ± 0.0009), reaching large effect level (t = 8.24, p = 1.23e-8, Cohen’s d = 0.89, 95% CI[0.0041,0.0137]); in the associative layer, degree centrality of high-propagation colors (0.0157 ± 0.0089) significantly exceeds ordinary colors (0.0066 ± 0.0034), representing medium to large effect (t = 5.43, p = 2.67e-6, Cohen’s d = 0.76, 95% CI[0.0059,0.0123]).

Inter-layer distribution testing of high-propagation colors employs two-proportion Z-test methods, showing extremely significant differences between perceptual layer high-propagation proportion (7.9%, 27/341) and associative layer proportion (1.9%, 34/1802) (Z = 6.24, p = 4.56e-10). Perceptual layer high-propagation density is 4.16 times that of the associative layer, reflecting propagation efficiency differences between different cognitive levels and validating systematic influence of cognitive complexity on propagation performance.

Table 3 Network position-propagation association measurements.
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Network position and propagation effect association measurements reveal core findings of hierarchical association patterns (Table 3). Perceptual layer PageRank shows extremely strong association with propagation frequency (r = 0.991), representing the highest value among all measurements. To validate this exceptionally strong correlation, we conducted comprehensive robustness checks. Edge permutation analysis (1,000 iterations) confirmed the association is not a statistical artifact (permutation p<0.001), with 97.8% of randomized networks showing correlations below r = 0.95. Frequency-controlled regression demonstrated PageRank remains a significant predictor (\(\beta\) = 50,346, p<0.001) after controlling for degree centrality, explaining additional variance beyond raw connectivity. Conservative high-frequency exclusion analysis removing the top 5% most frequent colors yielded a robust correlation of r = 0.882, while stratified analysis revealed that network centrality effects operate through a hierarchical mechanism where high-frequency basic colors serve as network hubs that amplify cognitive accessibility advantages, consistent with dual-process theories where simple concepts benefit more from structural positions. These robustness checks confirm that the observed association represents genuine structural effects reflecting cognitive accessibility advantages rather than frequency artifacts. This indicates that network centrality in basic cognitive layers has strong association with propagation effects. Inter-layer comparison employs Fisher’s r-to-Z transformation test, showing extremely significant differences between perceptual and associative layers (Z = 22.18, p = 1.16e-108), with perceptual layer indicators demonstrating significantly stronger association with propagation effects. This pattern correlates with network density characteristics: centrality indicators in low-density networks have higher discriminatory power, while association effects in medium-density networks (associative layer 0.101) are relatively weaker.

Comprehensive analysis results of color propagation effect network-based explanation are shown in Fig. 3, intuitively displaying propagation weight optimization testing, centrality advantage measurement, network position and propagation effect association patterns, and association strength comparison across different cognitive levels, validating the important role of network structural positions on propagation effects.

Fig. 3
figure 3

Propagation network analysis results: a Weight optimization testing, b Centrality advantage measurement, c Position-propagation association, d Inter-layer association comparison.

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Association discovery between product types and color patterns

Product clustering analysis determines a 5-category classification structure (Table 4) , with 2,252 products allocated as: lifestyle products 647, cosplay fashion 441, cultural creative peripherals 532, figure collections 115, and content media 517. Post numbers involved in each category show figure collection having highest participation (5,183 posts, 13.4%), followed by content media (3,892 posts, 10.1%) and cosplay fashion (3,469 posts, 9.0%), with lifestyle products and cultural creative peripherals having relatively lower participation.

Table 4 Product Category Distribution Statistics.
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Product-color association strength measurements based on 34,513 co-occurrence data from 14,533 valid posts identify 75 strong association combinations. Chi-square independence test confirms significant association between product categories and color choices (\(\chi ^2\) = 482.49, df = 76, p = 6.78e-91), with association strength reaching medium level (Cramér’s V = 0.237, 95% CI[0.221, 0.253]). Point-wise mutual information (PMI) analysis reveals differentiated color preferences among product categories: lifestyle products have highest PMI value 2.135 (purple magnolia, space silver gray, cherry blossom color), cultural creative peripherals PMI value 2.040 (colorful glass), cosplay fashion, content media, and figure collection have highest PMI values of 1.498, 1.326, and 1.185 respectively, embodying color semantic gradients from lifestyle to professional applications.

Cognitive hierarchy usage pattern analysis shows significant differences among product categories. Perceptual layer usage rates are relatively stable across categories (83.6–87.7%, standard deviation 0.015), with cosplay fashion having highest usage rate (87.7%) and cultural creative peripherals lowest (83.6%). Associative layer usage rates show greater variation (19.9–28.8%, standard deviation 0.029), with lifestyle products having highest usage rate (28.8%) and figure collection lowest (19.9%). Symbolic layer usage rates are generally low but with highest coefficient of variation (0.7–1.6%, coefficient of variation 0.368), with lifestyle products having highest usage rate (1.6%) and figure collection lowest (0.7%). Absolute usage statistics show perceptual layer dominance (17,477 times), followed by associative layer (3601 times), and symbolic layer least used (128 times), validating hierarchical characteristics of ACG color cognition in product applications.

Comprehensive analysis results of product type and color pattern associations are shown in Fig. 4, clearly displaying product category distribution characteristics, association strength analysis, cognitive level usage difference comparison, and PMI value distribution patterns, validating the systematic associations between ACG product types and color semantic hierarchies.

Fig. 4
figure 4

Product color association measurement results: a Product category distribution, b Association strength analysis, c Cognitive layer usage comparison, d PMI value distribution characteristics.

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Discussion

Network-based characterization discovery of cognitive processing complexity in digital environments

Three-layer color semantic networks constructed based on large-scale social media data reveal network representation differences of cognitive processing complexity in digital environments. Perceptual, associative, and symbolic layers exhibit systematic structural differences, validating the effectiveness of the three-layer analysis framework based on cognitive complexity.

Three-layer network structures present a dual pattern of“scale reduction-power concentration”: node numbers decrease from 165 to 71, while maximum degree centrality increases from 0.134 to 0.257, reflecting deep mechanisms of color cognitive processing complexification. The perceptual layer’s wide accessibility based on direct color identification transforms into extensive network connection capabilities, while the symbolic layer’s exclusivity dependent on culturally specific encoding leads to formation of authoritative nodes. Treisman’s9 feature integration theory indicates that cognitive processing hierarchy differences reflect different information processing mechanisms, and this study’s network measurements provide structural evidence for this.

Progressive network density reveals structural transformation mechanisms of color cognitive processing. Average clustering coefficient significantly decreases from 0.656 in the perceptual layer to 0.482 in the symbolic layer, indicating that cognitive complexification accompanies fundamental reorganization of association patterns. High clustering characteristics of the perceptual layer correspond to Zeng’s30 proposed “similarity aggregation effect,”where users establish close associations based on visual similarity; low clustering characteristics of the symbolic layer reflect“holistic framework dependency”mechanisms, where high-level color cognition relies more on overall cultural context rather than local similarity relationships, resonating with Gibson’s affordance concept31.

The unique bridging function of the associative layer embodies network-based expression mechanisms of color cognitive relationships in digital environments. The associative layer demonstrates critical cross-layer connection roles while exhibiting highest modularity (0.758), with these“high cohesion-strong bridging”characteristics revealing mediating functions of functional associations. Gradient distribution of inter-layer connection strength further validates research on bridging mechanisms between concepts in cognitive science32: intermediate abstract concepts play key roles in connecting concrete experience with abstract theory.

Differentiated community structure patterns in the symbolic layer embody“semantic cohesion effects”in cognitive abstraction processes. Though having fewest communities but highest intra-community edge ratio (0.892), this reflects color associations tending to form highly cohesive but relatively independent meaning communities, corresponding to Hughes et al.’s33 findings that culturally specific color usage closely relates to cultural identity. The perceptual layer contributes 49.6% of bridging nodes, indicating that basic perception undertakes“cognitive translation” functions in digital cultural propagation, reducing understanding barriers between different cultural groups through intuitive visual expression, consistent with Noy’s34 discussion of visual media’s role in participatory culture.

Association analysis of color semantic network position and propagation effects

Association analysis of network position and propagation effects reveals structural regularities of color propagation in digital environments. Extremely strong association between perceptual layer PageRank and propagation frequency (r = 0.991) compared to moderate association of associative layer centrality indicators (r = 0.427) reflects differentiated manifestations of cognitive complexity in digital propagation structures. The network science significance of extremely high correlation in the perceptual layer lies in revealing tight coupling relationships between network structure and functional performance in basic cognitive hierarchies. Network topological structure analysis indicates that node structural positions have important influences on network behavior35, and in sparse but structured network environments with relatively low network density (0.092), concepts based on direct color identification show highly deterministic propagation associations when occupying key bridging positions.

Differentiated influences of network density on centrality association strength extend cognitive dimensions of existing network propagation theory. Perceptual layer network density (0.092) is significantly lower than associative layer (0.101), with sparsity making bridging roles of key nodes more prominent, dialoguing with Granovetter’s weak tie theory36: sparse connections enhance propagation control efficacy of central nodes by reducing redundant pathways. Propagation performance differences in cognitive complexity validate applicability of Sweller’s cognitive load theory37 in digital propagation fields: perceptual layer high-propagation color proportion (7.9%) significantly exceeds associative layer (1.9%), with this 4.16-fold difference reflecting systematic associations between cognitive simplicity and network position mechanisms, demonstrating propagation advantage characteristics and providing network structure-level validation for Kahneman’s fast cognitive system advantages38.

Gradient distribution patterns of inter-layer network associations provide network science empirical extensions for Collins & Loftus’s spreading activation theory12. Connection strength gradient patterns of perceptual-associative layer (2.32) higher than perceptual-symbolic layer (1.80) and associative-symbolic layer (1.43) are consistent with distance decay effects of concept activation in spreading activation theory, extending individual cognitive-level theory to network representations of group behavior. Stratified distribution characteristics of bridging nodes further support application of Freeman’s betweenness centrality theory24 in cognitive networks: the perceptual layer contributes 49.6% of bridging nodes, higher than associative layer (30.4%) and symbolic layer (20.0%), indicating mediating hub roles of basic cognitive hierarchies in cross-layer information propagation, challenging traditional assumptions that moderate complexity concepts have optimal bridging capabilities.

Validation of hierarchical distribution of propagation weights and network position association strength forms complete explanations of cognitive economy mechanisms. The “sharing\(\approx\)liking>commenting” weight hierarchy not only validates advantages of lightweight participation in social media but reveals systematic associations between low cognitive cost interaction methods and network centrality of simple concepts. Extremely strong correlation of perceptual layer network position indicators validates Wasserman & Faust’s39 core assumptions about positional influence, indicating that cognitively simple concepts obtain relatively independent propagation advantages through network structures.

Position-propagation association patterns in color semantic networks reflect network-based implementations of cognitive psychology principles in digital environments: structural propagation advantages of the perceptual layer validate network amplification effects of cognitive economy principles, mediating functions of the associative layer extend cognitive applications of structural hole theory, and exclusive characteristics of the symbolic layer provide network structure microfoundations for cultural propagation. This discovery provides theoretical basis and empirical support for ACG color design strategies based on network science.

ACG color design strategies based on cognitive anomaly effects

Based on the cognitive complexity three-layer framework, this study identifies several anomalous phenomena in network analysis data, providing new approaches for ACG color design that differ from traditional strategies.

The associative layer network simultaneously possesses highest modularity (0.758) and strong bridging functions, providing data foundations for mediation mechanisms in ACG cultural propagation. Associative layer colors (such as cherry blossom pink, sky blue) maintain semantic connections with basic colors while carrying specific cultural connotations, giving them unique value in connecting mainstream users with core ACG users. In ACG product design, this mediation effect is particularly suitable for products targeting pan-ACG users: anime merchandise, light ACG games, ACG-style lifestyle products, etc. Connection strength of 2.32 indicates that using associative layer colors may find balance points between cultural expression and mass acceptance.

Extremely low usage frequency of symbolic layer colors (Hatsune green 23 times) contrasts with their important status in ACG communities, revealing scarcity value mechanisms of subculture symbols. This scarcity provides strategic thinking for cultural identification of core ACG products: limited edition coloring for figures, character-specific colors for cosplay costumes, brand identification for ACG IPs, etc. In specific applications, symbolic layer colors should only be used for the most important cultural identification nodes, such as character theme colors, cultural event identifications, core fan exclusive designs, etc., avoiding use in decorative elements to maintain their cultural exclusivity.

Extremely strong association between perceptual layer PageRank and propagation effects (r = 0.991) provides correlational evidence for digital propagation of ACG content. In ACG social media propagation, anime content promotion, fan work display and other scenarios, perceptual layer colors (such as blue, white, red) show strong association with high propagation effects. This strategy is particularly suitable for ACG content needing rapid breakthrough: viral anime memes, ACG culture popularization content, anime promotion targeting general audiences, etc.

Gradient distribution of inter-layer connection strength (2.32\(\rightarrow\)1.80\(\rightarrow\)1.43) provides pathway references for cultivating ACG users’ cultural cognition. The transformation process from casual users to core fans can adopt progressive color guidance from perceptual layer\(\rightarrow\)associative layer\(\rightarrow\)symbolic layer: initially using perceptual layer colors to attract attention, building cultural interest through associative layer colors, and finally achieving deep cultural identification through symbolic layer colors. This strategy has application value in ACG content user education, fan community building, cultural IP cultivation, etc.

Differences in three-layer color usage across different ACG product types provide guidance for specific applications. Low symbolic layer usage rate in figure collection products (0.7%) suggests their high requirements for cultural exclusivity, warranting focus on character-specific colors for precise identification; high perceptual layer usage rate in cosplay fashion products (87.7%) reflects their need to balance character restoration with mass aesthetics; high associative layer usage rate in ACG lifestyle products (28.8%) indicates their consideration of daily usage acceptance while maintaining cultural identification.

Three-layer color characteristics may play different roles across various ACG digital platforms. On pan-ACG platforms like Bilibili and Weibo, perceptual layer colors facilitate rapid content propagation and breakthrough; on professional ACG forums and fan communities and other core platforms, symbolic layer colors can strengthen cultural identification and group belonging; on anime official platforms and IP promotion channels, associative layer colors can balance cultural expression with commercial promotion needs.

Anomaly effect analysis based on the cognitive complexity three-layer framework provides culturally sensitive strategy references for ACG color design. Through identifying special patterns in network data, designers can optimize propagation effects while maintaining subculture characteristics, providing scientific color strategy support for sustainable development of the ACG cultural industry.

Research limitations and future directions

This study achieves important progress in ACG color cognitive network analysis but still has limitations that need consideration in result interpretation, while these limitations also point to important future research directions.

Data sources limited to Chinese social media platforms indeed restrict direct cross-cultural generalization of research results. Color semantics possess cultural specificity, with symbolic layer colors such as“Hatsune green”and“yandere pink”in this study potentially having different connotations or lacking corresponding concepts in other cultural environments. Though theoretical foundations of cognitive hierarchical classification have universality, specific color classifications and semantic contents require revalidation in different cultural backgrounds. This limitation requires caution when applying research results to non-Chinese ACG environments and necessitates corresponding localization adjustments.

Limited symbolic layer node numbers (71) objectively reflect scarcity of subculture concepts but indeed affect robustness of statistical analysis for this hierarchy. Small sample sizes may lead to instability of certain network indicators in the symbolic layer, particularly when making statistical comparisons with other hierarchies. Additionally, manual annotation based on 5000 samples, while establishing classification standards, may not adequately cover rapidly evolving ACG color concepts, risking omission of emerging color semantics.

Network construction methods based on textual co-occurrence have inherent limitations. This method cannot directly measure users’ visual perceptual reactions and emotional experiences, potentially missing important non-linguistic color cognitive processes. Simultaneously, textual expressions may be influenced by individual user differences, platform characteristics, and social norms, not completely equivalent to actual color cognitive structures. These methodological limitations need compensation through integration of physiological measurements and behavioral experimental data.

Static network analysis fails to capture dynamic evolution processes of ACG color semantics, representing obvious deficiency in rapidly changing digital cultural environments. Color popularity trends, semantic transformations, and propagation patterns may undergo significant changes in short periods, while current analysis frameworks cannot reflect these temporal characteristics. Furthermore, research primarily reveals correlational relationships between network position and propagation effects, lacking rigorous causal validation, limiting certainty of strategy recommendations.

Despite these limitations, the methodological framework established by this study provides important foundations for subsequent research. Future research should focus on four directions: first, validating cross-cultural applicability of cognitive hierarchical principles through multi-linguistic, multi-cultural platform comparative studies; second, integrating eye-tracking, brain imaging, and other multi-modal data to establish direct connections between network structures and cognitive processes; third, developing dynamic network analysis methods to track temporal evolution trajectories of color semantics; finally, designing controlled experiments to validate causal influences of network position on propagation effects.

These research extensions will not only address current limitations but advance digital cultural cognitive analysis toward more precise and comprehensive directions, providing more reliable scientific guidance for cultural creative industries. Though current research has deficiencies, the established theoretical framework and analysis methods lay important foundations for this emerging field, with value to be fully realized through continuous improvement in subsequent research.

Conclusion

This study establishes a cognitive complexity-based color semantic network analysis framework, integrating feature integration theory, ecological perception theory, and cultural semiotics theory to achieve quantitative characterization of ACG color cognition. Analysis of 38,566 social media data points validates systematic associations between cognitive complexity and network structural characteristics.

Research findings confirm hierarchical network representation of cognitive processing complexity in digital environments. The three-layer framework exhibits a“scale reduction-power concentration”pattern, with network nodes decreasing from 165 to 71 while maximum degree centrality increases from 0.134 to 0.257. Strong association between network position and propagation effects (r = 0.991) provides network science explanations for cognitive simplicity’s transmission advantages and confirms strong association between structural positions and propagation effects.

Methodological contributions include operationalized conversion from cognitive psychology theory to complex network analysis, providing new analytical tools for quantitative research of abstract cognitive concepts. Multi-layer network analysis reveals cross-layer connection mechanisms through 1709 bridging nodes, with the associative layer’s unique bridging functions validating mediation roles of functional concepts in cultural propagation. This research demonstrates that cognitive complexity systematically transforms into network topological characteristics, extending cognitive theory applications in digital cultural research.

Application value is validated through differential analysis across ACG product types. Usage patterns of figure collection, cosplay fashion, and lifestyle products provide data-driven segmentation strategies for ACG color design, enabling transformation from experiential judgment to cognitive science guidance in cultural creative industries.

This study provides empirical foundations for understanding network propagation mechanisms of cultural cognition in the digital age, contributing to methodological development of cultural cognitive network science. Future research should extend to multi-linguistic environments and integrate neuroimaging technology to establish causal associations between network characteristics and cognitive processing.