Complex Network Analysis Techniques

A molecular tree is defined as a tree in which no vertex has degree exceeding 4. Consider such a tree T with edge set E. For each vertex u in T, let d(u) represent its degree. In this paper, we study a class of molecular descriptors defined by Bf(T) = ∑︁ uv∈E f(d(u),d(v)), where f is a symmetric real-valued function t…

Degree-based graph entropies quantify structural heterogeneity by transforming vertex-degree information into a probability distribution and applying Shannon entropy. We develop a unified framework for three Prodeg-type degree-power invariants, namely the Inverse Prodeg index [Formula: see text], the Misbalance Prodeg…

Graph-theoretic degree-based descriptors play a central role in chemoinformatics and QSPR/QSAR modelling, yet most classical indices either focus purely on vertex degrees or treat bond contributions in a purely multiplicative way. In this work we introduce and systematically study a new family of modified bond-based i…

Topological indices play a fundamental role in the study of graph structures and their quantitative properties, particularly in applications related to chemistry, network science, and dynamic system analysis. In this work, we study the Reduced Zagreb index, Zagreb coindices, and the PI index of monogenic semigroup gra…

The Sombor index has recently become a central tool among degree-based graph invariants; however, it does not explicitly isolate degree imbalance along edges. In this work, we introduce the degree-based Contrastive Sombor Index (CSO), which combines endpoint-degree magnitude with local degree imbalance. For a finite s…

Short-form video content has gained importance as a popular form of digital media due to the rising popularity of social media platforms and the decreasing attention spans of consumers. However, a major obstacle to popularity detection in short-form content is the heterogeneous nature of the data, encompassing textual…

Graph descriptors such as normalized Laplacian energy, Sombor index, Mostar index and Zagreb index are often employed in various scientific contexts. The Sombor index is essential in chemical graph theory because it provides insights into molecule stability and reactivity by analyzing the distribution of atom degrees…

This study presents a theoretical analysis of partitional clustering on networks, analyzing both hard and soft assignment schemes with different objective functions. Cluster centers are not restricted to vertices but can also be located along the edges. We examine four key models: P-Median (PMP) and Sum of Squares Clu…

This study presents a theoretical analysis of partitional clustering on networks, analyzing both hard and soft assignment schemes with different objective functions. Cluster centers are not restricted to vertices but can also be located along the edges. We examine four key models: P-Median (PMP) and Sum of Squares Clu…

The rapid growth of meme cryptocurrencies has raised concerns about speculative contagion within the broader cryptoasset market. While prior studies examine bubble behaviour in individual cryptocurrencies, little is known about how speculative regimes propagate between meme coins and major cryptoassets. This study ana…

Topological indices are mathematical tools that numerically express the topological properties of molecular structures that can be represented by graphs. These indices are widely used in various disciplines such as biology, computer science, and network theory, as well as chemistry. In graph theory, many topological i…

Sosyal ağ analizinin odak noktası, sosyal varlıklar arasındaki ilişkileri incelemektedir. Farklı alanlarda kullanılan sosyal ağ analizi eğitim alanında yaygın olarak kullanılmaktadır. Sosyal ağın analiziyle elde edilen ölçüm sonuçları, öğrencilerin öğrenme etkinlikleri ile ilişkisinin anlaşılmasına ve öğrencilerin öğr…