Graph representations (adjacency matrix, edge list, CSR/CSC), Directed/undirected/multigraphs, Basic metrics (degree, density, diameter, average path length), Connected components and strongly connected components, Gr...
Graph representations (adjacency matrix, edge list, CSR/CSC), Directed/undirected/multigraphs, Basic metrics (degree, density, diameter, average path length), Connected components and strongly connected components, Graph isomorphism and canonical labeling, Bipartite graphs and projections.
Degree centrality variants (in-degree, out-degree, weighted), Closeness centrality and harmonic mean, Betweenness centrality (Brandes algorithm), Eigenvector centrality and Katz matrix, PageRank (power iteration, personalized, topic-sensitive), HITS (authority/hub scores), SALSA improvement.
Modularity optimization and Louvain method, Spectral clustering (normalized Laplacian), Label propagation algorithm, Infomap (random walks), Clique percolation method, Overlapping communities (CPM, SLPA), Hierarchical clustering (single-linkage dendrograms), Benchmark networks (LFR generator).
Frequent subgraph mining (Apriori-based, gSpan), Graph motif discovery and network motifs, Graphlet counting and degree distributions, Triangle counting and enumeration, Graph kernels (graphlet, shortest-path, Weisfeiler-Lehman), Subgraph matching and isomorphism testing, Graph alignment.
Small-world phenomenon and clustering coefficient, Scale-free networks and power-law distributions, Link prediction (common neighbors, Jaccard, Adamic-Adar, Katz, matrix factorization), Influence maximization (greedy algorithm, TIM/CELF), Cascade models (Independent Cascade, Linear Threshold), Signed networks and balance theory, Temporal networks and dynamic analysis.