Complex Networks

Reproducing the first and second moment of empirical degree distributions ArXiv ID: 2505.10373 “View on arXiv” Authors: Mattia Marzi, Francesca Giuffrida, Diego Garlaschelli, Tiziano Squartini Abstract The study of probabilistic models for the analysis of complex networks represents a flourishing research field. Among the former, Exponential Random Graphs (ERGs) have gained increasing attention over the years. So far, only linear ERGs have been extensively employed to gain insight into the structural organisation of real-world complex networks. None, however, is capable of accounting for the variance of the empirical degree distribution. To this aim, non-linear ERGs must be considered. After showing that the usual mean-field approximation forces the degree-corrected version of the two-star model to degenerate, we define a fitness-induced variant of it. Such a `softened’ model is capable of reproducing the sample variance, while retaining the explanatory power of its linear counterpart, within a purely canonical framework. ...

Mitigating Extremal Risks: A Network-Based Portfolio Strategy ArXiv ID: 2409.12208 “View on arXiv” Authors: Unknown Abstract In financial markets marked by inherent volatility, extreme events can result in substantial investor losses. This paper proposes a portfolio strategy designed to mitigate extremal risks. By applying extreme value theory, we evaluate the extremal dependence between stocks and develop a network model reflecting these dependencies. We use a threshold-based approach to construct this complex network and analyze its structural properties. To improve risk diversification, we utilize the concept of the maximum independent set from graph theory to develop suitable portfolio strategies. Since finding the maximum independent set in a given graph is NP-hard, we further partition the network using either sector-based or community-based approaches. Additionally, we use value at risk and expected shortfall as specific risk measures and compare the performance of the proposed portfolios with that of the market portfolio. ...

Complex network analysis of cryptocurrency market during crashes ArXiv ID: 2405.05642 “View on arXiv” Authors: Unknown Abstract This paper identifies the cryptocurrency market crashes and analyses its dynamics using the complex network. We identify three distinct crashes during 2017-20, and the analysis is carried out by dividing the time series into pre-crash, crash, and post-crash periods. Partial correlation based complex network analysis is carried out to study the crashes. Degree density ($ρ_D$), average path length ($\bar{“l”}$), and average clustering coefficient ($\overline{“cc”}$) are estimated from these networks. We find that both $ρ_D$ and $\overline{“cc”}$ are smallest during the pre-crash period, and spike during the crash suggesting the network is dense during a crash. Although $ρ_D$ and $\overline{“cc”}$ decrease in the post-crash period, they remain higher than pre-crash levels for the 2017-18 and 2018-19 crashes suggesting a market attempt to return to normalcy. We get $\bar{“l”}$ is minimal during the crash period, suggesting a rapid flow of information. A dense network and rapid information flow suggest that during a crash uninformed synchronized panic sell-off happens. However, during the 2019-20 crash, the values of $ρ_D$, $\overline{“cc”}$, and $\bar{“l”}$ did not vary significantly, indicating minimal change in dynamics compared to other crashes. The findings of this study may guide investors in making decisions during market crashes. ...