Node Metrics in Complex Networks: Foundations, Perspectives and Applications
Speaker: Sergey Shvydun
Abstract: Understanding the structural role of nodes in complex systems is crucial for identifying influential individuals in social networks, critical components in infrastructure, essential proteins in biological networks and high-impact pages or users in information networks. Over the years, a large number of node metrics have been proposed to capture different aspects of network structure. However, the abundance of available metrics has introduced significant challenges, particularly in selecting, comparing and validating these measures. In this talk, we will review existing approaches for quantifying structural roles and their applications, discuss key challenges and limitations and present an interactive platform for exploring and comparing graph metrics.
[ Slides ]
Matched Topological Subspace Detector
Speaker: Chengen Liu
Abstract: Topological spaces, represented by simplicial complexes, capture richer relationships than graphs by modeling interactions not only between nodes but also among higher-order entities, such as edges or triangles. This motivates the representation of information defined in irregular domains as topological signals. By leveraging the spectral dualities of Hodge and Dirac theory, practical topological signals often concentrate in specific spectral subspaces (e.g., gradient or curl). For instance, in a foreign currency exchange network, the exchange flow signals typically satisfy the arbitrage-free condition and hence are curl-free. However, the presence of anomalies can disrupt these conditions, causing the signals to deviate from such subspaces. In this work, we formulate a hypothesis testing framework to detect whether simplicial complex signals lie in specific subspaces in a principled and tractable manner. Concretely, we propose Neyman-Pearson matched topological subspace detectors for signals defined at a single simplicial level (such as edges) or jointly across all levels of a simplicial complex. The (energy-based projection) proposed detectors handle missing values, provide closed-form performance analysis, and effectively capture the unique topological properties of the data. We demonstrate the effectiveness of the proposed topological detectors on various real-world data, including foreign currency exchange networks.
[ Slides ]