Topology in Complex Networks: Insights from Topological Data Analysis

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Explores Eulerian circuits through the Königsberg bridges problem, leading to the development of graph theory and topology.

Introduces the fundamentals of network science, focusing on brain networks and their historical breakthroughs.

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Covers the definition of flow in a network and flow calculation.

Covers the fundamentals of handling networks and centrality measures in graph theory.

Explores non-parametric regression for networks, covering object data analysis, network graphs, extrinsic distances, and practical projections.

Covers the Stochastic Block Model and its application in community detection, exploring its mathematical formulation and challenges.

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Explores knowledge inference for graphs, discussing label propagation, optimization objectives, and probabilistic behavior.

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.