Background: Network science has evolved into a foundational paradigm for understanding complex systems across domains ranging from social interactions to biological metabolism and technological infrastructures. Foundational works on small world networks, scale free topologies, and community structures have revealed universal structural regularities in complex systems. Simultaneously, digital traces generated through online platforms have enabled large scale empirical investigations of social media, collaboration networks, and culinary datasets. Recent research demonstrates that food recipes, ingredient co occurrence networks, and digital culinary interactions exhibit structural patterns analogous to those found in social and technological networks. However, existing scholarship often treats these domains in isolation, leaving an integrative theoretical framework underdeveloped.

Objective: This study develops a unified theoretical and empirical framework that integrates classical network science with computational social systems and culinary network analysis. Drawing exclusively from established literature in network topology, small world theory, scale free networks, community detection, anomaly detection, diffusion processes, and recipe datasets, the article synthesizes theoretical foundations and applies them to ingredient networks, social diffusion, and information credibility systems.

Methods: The methodology integrates structural network analysis, community detection using modularity based and refined algorithms, clustering coefficient estimation, random walk based sampling, centrality analysis, and content driven computational methods including natural language processing. Empirical grounding is derived conceptually from recipe datasets, biomedical collaboration networks, and social media datasets. Ingredient networks are modeled as co occurrence graphs, and theoretical insights from scale free and small world models are applied to analyze connectivity, diffusion, robustness, and substitution dynamics. Rumor detection and anomaly detection frameworks are incorporated to examine information integrity in food related and social media contexts.

Results: The analysis demonstrates that ingredient networks exhibit scale free characteristics, high clustering, and short path lengths consistent with ultrasmall properties. Community structures correspond to regional cuisines and functional ingredient clusters. Opinion leader theory and eigenvector centrality illuminate diffusion of culinary innovations and dietary trends. Knowledge graph approaches enable structured ingredient substitution modeling. Social media analytics reveal how emerging topics in food discourse propagate through temporally and structurally constrained networks. Theoretical extrapolation suggests that culinary ecosystems mirror biological metabolic networks and technological infrastructures in both topology and vulnerability.

Conclusion: The convergence of network science, computational social systems, and culinary data analytics reveals a coherent structural paradigm governing heterogeneous complex systems. By integrating ingredient networks with theories of diffusion, anomaly detection, and community detection, this work advances a unified interpretative framework. Future research should deepen cross domain modeling, develop longitudinal network evolution models, and integrate semantic and structural features for enhanced interpretability and resilience.