Le3 - Wed Oct 9, 2024 Degree centrality; Power law versus Poisson distribution; Estimation methods for the degree exponent: ML approach; Explaining the power law; Erdos-Renyi random model: binomial and Poisson descriptions of the model; Small world; Power law versus Poisson distribution; Growth and preferential attachment; the Barabasi-Albert model.
Le4 - Fri Oct 11, 2024 Attractiveness and the Bianconi-Barabasi model; Analysis of the Bianconi-Barabasi model; Examples with equal and uniform fitness; Measuring fitness: the www; Other ideas for modelling the power-law, Properties of the power-law: largest hub, moments and scale-free networks, distances; PageRank: random walk, dead ends and spider traps, teleportation; PageRank with restart.
Le5 - Wed Oct. 16, 2024 PageRank versus degree centrality; convergence properties of PageRank; PageRank matrix structure via the condensation graph; Action of the teleport vector: one leaf-only, one eigenvalue set to 1 and the rest to (at most) c; Interpretation; Tuning the teleport vector: Local PageRank; Examples of application; Approximate PageRank and the push operation.
Le6 - Fri Oct. 18, 2024 Approximate PageRank and the push operation: proof of the precision guarantee; Application to link prediction; Topic specific PageRank; Signed PageRank; Preventing spamming; Row-normalized PageRank; HITs centrality.
Le7 - Wed Oct 23, 2024 Eigenvector and Katz centralities and their relation to PageRank and Degree centrality; Closeness and harmonic centrality; Betweenness centrality as a measure of brokerage; The clustering coefficient; Wrap-up on centrality measures.