Robustness in complex networks reflects the capacity of a system to maintain connectivity and essential functionality under random failures or deliberate attacks. Accurately assessing how structural properties influence resilience is critical for designing stable infrastructures and preventing cascading disruptions. Traditional robustness analyses often rely on random or degree-based node removals, but these approaches remain insufficient at capturing the spatial dispersion and topological diversity that shape real-world network vulnerability. This study investigates network robustness under non-adaptive, semi-adaptive, and fully adaptive node removal strategies using two recently proposed dispersion-oriented measures: Farthest-First (FF) traversal and Farthest-First intrapartition Degree Centrality (FFiDC). These methods prioritize nodes based on structural separation and intra-community significance, offering a complementary perspective to conventional centrality-driven dismantling. We evaluate their effectiveness in fragmenting network connectivity across both synthetic and real-world networks using the Largest Connected Component (LCC) as the primary robustness metric. Results show that the FFiDC approach surpasses or performs at-par with traditional degree-based strategies in reducing the LCC, particularly in adaptive scenarios. The semi-adaptive framework provides a favorable balance between computational efficiency and dismantling performance, preserving much of the adaptive strategy’s strength with significantly reduced overhead. The results show that the proposed FFiDC approach under semi-adaptive node removal strategy consistently reduces the execution time across all network models and configurations. The runtime reduction ranges from 5.1% to 27.5% for Barabási–Albert (BA) networks, 4.0% to 24.8% for Erdös–Rényi (ER) networks, and 10.5% to 23.9% for Watts–Strogatz (WS) networks.
Understanding the association between social connections and individual psychological traits is critical for educational administrators. Existing studies rely heavily on online questionnaires, web-scraped media data, and self-reported surveys, whereas analyses of offline social networks and mental health remain scarce. By leveraging a public dataset encompassing on-campus dining activities over 21 weeks, we construct student co-dining networks and track how their topology changes over time. Empirical analysis reveals that node centrality in the co-dining networks is significantly and positively correlated with improvement in the flourishing trait–a core construct of positive mental well-being. Furthermore, students with more connections tend to show greater improvement in the flourishing trait. Our findings offer potential guidance to assist students in maintaining positive mental health.
Historically, languages struggle to maintain their existence by retaining their speakers. With the recent attention and extensive literature on the topic, bilingualism is widely discussed as a means to preserve minority languages. Although the literature recognizes bilinguals as a group and some language models explicitly incorporate them, they are still often portrayed primarily as a transitional stage in language acquisition. Our work advances this literature by treating bilinguals as a distinct speaker class within a three-state modeling framework, defined by their own identity and social status. We analyze the stability and long-term persistence of this group under different social and demographic conditions. We further illustrate the model using Manx language data, showing how a bilingual minority community contributed to the revival of a language once considered extinct.
In this paper, we present a graph-theoretic framework for assessing the connectivity and structural impact of single-point mutations in biological enzymes. The method maps the three-dimensional crystallographic structure of a given enzyme into a [Formula: see text]-Protein Residue Network (PRN), where nodes [Formula: see text] represent central [Formula: see text] carbons in amino acids and edges represent physical interactions. We quantify residue relevance via centrality measures; in particular, we focus on betweenness, closeness, and eigenvector centralities. In silico mutagenesis (node impairment) is then applied to simulate single-point mutations. Using the SARS-CoV-2 main protease (M pro ) as a model, we analyze both apo and inhibitor-bound (holo) states. Our analysis identifies betweenness centrality as the most sensitive metric to perturbation. We show that simulated disruption of the catalytic residue Cys145 causes profound network disconnection, an effect amplified over tenfold in the holo state. Furthermore, we find that perturbation of the allosteric “160-loop” residue His164 rivals the effect of mutating the catalytic His41, underscoring its role as a critical hub for dimer stability and long-range communication. This network-based approach provides a rapid, topology and connectivity-driven strategy to analyze and target potential active and allosteric sites, offering a complementary tool for guiding targeted drug design.
Topological data analysis offers techniques for uncovering structure in highdimensional datasets, with persistent homology and the Mapper algorithm being two widely used methods. Persistent homology captures topological features across filtration scales, while Mapper constructs a graph-based summary of the data at a chosen resolution. In this paper, we apply both methods to the Wisconsin Breast Cancer Dataset in order to compare the type of structural information each method provides. Rather than treating persistent homology and Mapper as competing tools, we frame them as complementary approaches. Persistent homology summarizes the underlying shape of the data across different scales, while Mapper highlights clustering structure, local connectivity, and regions where benign and malignant samples exhibit overlapping characteristics in the feature space. We further support the visual persistent homology analysis using Wasserstein distances between persistent diagrams. Together, persistent homology and Mapper provide complementary topological perspectives on the same data: persistent homology identifies a quantitatively distinct topological structure between the benign and malignant groups (quantified via the 1-Wasserstein distance), while Mapper localizes where this difference manifests in the data as transition zones and class-dominated subgraphs. Neither method alone provides both the global algebraic summary and the local graph-level resolution that the combined analysis yields.
