arXiv subjects

Hrishidev Unni

Publications and source records attributed to Hrishidev Unni.

4 recordsLinked to original sources

arXiv2026

Spectral and Eigenvector Crossovers in Random Mixed Graphs

We study the spectral and eigenvector properties of random mixed graphs, combining undirected and directed interactions, using random matrix theory (RMT). The network is represented by a Hermitian adjacency matrix, with undirected links as real entries and directed links as purely imaginary conjugate pairs, ensuring a real spectrum. Network density is controlled by the connection probability, while directionality sets the fraction of directed edges. We focus on the GOE-to-GUE crossover: at fixed connectivity, increasing directionality breaks time-reversal symmetry and drives spectral statistics from GOE to GUE. We show that this transition requires sufficient connectivity. In sparse networks, weak level repulsion produces Poisson statistics regardless of directionality. At fixed directionality, increasing connectivity drives a Poisson-to-GUE crossover; only above a sparsity threshold does the directionality-induced GOE-to-GUE transition emerge. In the dense regime, where the spectral density follows the Wigner semicircle law, the crossover is characterized using spacing distributions, spacing ratios, and spectral rigidity. In sparse networks, where unfolding is unreliable, spacing-ratio statistics provide an unfolding-free characterization. Eigenvector structure is examined through multifractal dimensions and component distributions, while Kullback--Leibler divergence confirms the robustness of the transitions. Applied to S&P 500 mixed graphs, the framework reveals a GOE-to-GUE crossover across four major market crashes. Denser crisis periods show sharper crossovers than sparser recovery periods. The results provide a unified picture of how connectivity and symmetry breaking govern spectral and eigenvector universality, while providing a transparent probe of changing financial-market organization.

physics.comp-ph↗

arXiv2025

Biswas-Chatterjee-Sen (BChS) kinetic exchange opinion model on modular networks

We study opinion formation in a society where agents interact on a modular network generated using a stochastic block model (SBM). Opinion dynamics is modeled through the Biswas-Chatterjee-Sen (BChS) kinetic exchange model, in which agents undergo pairwise interactions that could be positive or negative. By tuning the relative strength of intra- and inter-group connectivity inherent to the SBM, as well as the disagreement probability, we identify distinct collective phases. In particular, we observe a robust regime with strong intragroup ordering but no global consensus, in addition to fully ordered and disordered states. In the particular case of two modules, we observe an anti-ferromagnetic type ordering with the increase of negative interaction between the groups. We show approximate analytical calculations and numerical results of it. These results demonstrate how modular interaction structure can qualitatively alter collective opinion dynamics and hinder consensus formation.

physics.soc-ph↗

arXiv2025

Breakthrough Asymmetries across Disciplines and Countries: A Network approach to Structural Complexity of Scientific Progress

Science is driven by community endeavors across diverse fields and specializations, forming a complex structure that renders conventional performance evaluation methods inadequate. Using established indicators, the network-based normalized citation score, and the disruptive index, combined with the GENEPY algorithm, we evaluate the complexity rank of countries based on their breakthrough performance across 89 subfields of physical sciences, drawing on nearly 60 million articles (1900-2023). This quality-focused integrated approach reveals pronounced asymmetries: while countries such as the United States, Israel, and several in Europe sustain long-term structural advantages, emerging nations show rapid gains in later decades. A power-law relationship between aggregated breakthrough performance and countries' R&D expenditure underscores the unequal and scale-dependent nature of global science. These results demonstrate that scientific advancement arises not from uniform growth but from asymmetric complexity, offering actionable insights for policymakers and funding agencies aiming to foster sustainable, high-quality research ecosystems.

cs.DL↗

arXiv2025

Analyzing the progress of Indian states chasing sustainable development goals using complex network framework

The Sustainable Development Goals (SDGs) offer a critical global framework for addressing challenges like poverty, inequality, climate change, etc. They encourage a holistic approach integrating economic growth, social inclusion, and environmental sustainability to create a better future. We aim to examine India's responsibility in achieving the SDGs by recognizing the contributions of its diverse states in the federal structure of governance. As the nodal agency in India, the NITI Aayog's existing SDG index, using various socioeconomic indicators to determine the performance across different goals, serves as a foundation for assessing each state's progress. Building on the seminal works of Hidalgo and Hausmann (2009) and Tachhella et al. (2012), which introduced the economic complexity/fitness index, Sciarra et al. (2020) proposed the SDGs-Generalized Economic Complexity (GENEPY) framework to quantify "complexity" by computing "ranks for states" and "scores for goals", treating them as part of a complex bipartite network. In this paper, we apply the SDGs-GENEPY, to evaluate the progress and evolution of Indian states and union territories over several years. This enables us to identify each state's capacity (and rank) in achieving the SDGs. We can interpret these complexity scores as "centrality measures" of a complex bipartite network of the states and the goals. This enhances our understanding of the complex relationship between state capabilities and the achievability of SDGs within the Indian context and enables data-driven policy-making.

econ.GN↗