Dinamik Sosyal Ağ Analizi için Esnek Trioid Grafikleri

Öz

Esnek trioid grafikleri, parametreleştirilmiş cebiri ve graf kuramını birleştirerek, değişen bağlamlar altında hem cebirsel yapı hem de ilişkisel bağlantısallık sergileyen sistemleri modellemek için kullanılır. Bu çalışma, söz konusu çerçeveyi dinamik sosyal ağ analizi alanına uygulamakta ve idempotent bir ağın yarı-kafes (semilattice) ayrışımının zamansal olarak kararlı topluluklar ürettiğini göstermektedir; burada idempotent elemanlar kalıcı etkileyiciler olarak işlev görür. Twitter verileri üzerinde gerçekleştirilen ampirik doğrulama, gerçek topluluk etiketleriyle %92 oranında uyum sağlamış ve Louvain (0.62), Infomap (0.65) ve dinamik stokastik blok modelleri (0.71) gibi geleneksel yöntemleri önemli ölçüde geride bırakmıştır. Ayrışım ayrıca hiyerarşik etki yapılarının varlığını ortaya koymakta olup, en üst düzey etkileyicilerin etkilerinin daha yavaş azaldığını göstermektedir. Bu bulgular, esnek trioid grafiklerinin bilimsel ve mühendislik alanlarında parametreleştirilmiş ilişkisel sistemlerin analizinde güçlü bir matematiksel araç olduğunu ortaya koymaktadır.

Anahtar Kelimeler

• Esnek trioid grafikleri
• parametreleştirilmiş sistemler
• erişim kontrolü
• sosyal ağlar
• ayrışım algoritmaları.

Soft Trioid Graphs for Dynamic Social Network Analysis

Öz

Soft trioid graphs integrate parameterized algebra with graph theory to model systems exhibiting both algebraic structure and relational connectivity under varying contexts. This paper applies the framework to dynamic social network analysis, demonstrating that semilattice decomposition of an idempotent network yields temporally stable com-munities, with idempotent elements serving as persistent influencers. Empirical valida-tion on Twitter data achieves 92% agreement with ground-truth community annotations, substantially outperforming traditional methods such as Louvain (0.62), Infomap (0.65) and dynamic stochastic block models (0.71). The decomposition further reveals hier-archical influence structures, with top-tier influencers exhibiting slow influence decay. These findings establish soft trioid graphs as a robust mathematical tool for analyzing parameterized relational systems across scientific and engineering domains.

Anahtar Kelimeler

• Soft trioid graphs
• parametrized systems
• access control
• social networks
• decomposition algorithms.

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