I will explain key concepts of random graphs theory

Random graphs are the math behind modern networks (social media, web links, biology, finance). I help you model, simulate, and understand these networks using Python clearly and without unnecessary jargon.

Topics I cover (basic advanced):

Graph fundamentals: degree, paths, components, clustering, centrality

Random graph models: ErdősRényi G(n,p), G(n,m), random regular graphs

Configuration model (given degree sequence)

Preferential attachment (scale-free behavior) + small-world (WattsStrogatz)

Random geometric graphs and directed networks

Thresholds: connectivity, giant component emergence, phase transitions

Network comparisons: real data vs random baselines, robustness tests

Stochastic Block Model (SBM) for community structure + parameter estimation

Random walks / Markov chains on graphs, diffusion and spreading processes

Spectral basics (Laplacian, eigenvalues) when useful

Monte-Carlo experiments, parameter sweeps, clear plots + short report

Deliverables: reusable Python code/notebook + visuals + a simple explanation of results.

Note: I provide analysis/tutoring/research support and do not complete graded work for submission.