Social Network Analysis: Lecture Notes

Typeset lecture notes for Social Network Analysis, University of Pisa, academic year 2024/25. The notes cover network science: basic measures and generative models, centrality and assortative mixing, tie strength and resilience, simplicial complexes and hypergraphs, community detection, the dynamics of temporal networks, link prediction, dynamic community detection, and diffusion (decision-based models, epidemics, and opinion dynamics).

⚠️ Disclaimer. Derived from the Social Network Analysis course materials (Academic Year 2024/2025), MSc in Data Science & Business Informatics, University of Pisa.

These notes are open educational content created by a student. They are not an academic source and may contain inaccuracies. You may freely share, modify, and reuse this material for educational and non-commercial purposes with appropriate attribution. The content is my personal interpretation of the professor's course materials and should not replace official teaching resources. I assume no responsibility for any errors or misinterpretations.

These notes were produced with an AI-in-the-middle workflow: a first human pass, then Claude Code to support formulation, understanding, and rewriting, followed by a final human review.

If you find errors, have suggestions, or spot unintentionally included copyrighted material (which I will promptly remove on notification), contact me at sclfnc@proton.me.

This course is part of the MSc Data Science lecture notes collection (University of Pisa), one repository per course. Clone the whole set with git clone --recursive.

Layout

• main.tex: entry point, in the folder root; identical across the whole notes collection (it only loads the shared preamble and the course file).
• src/housestyle.tex, shared house style: geometry, colors, section and ToC formatting, running heads, and the math environments (theorem, definition, …).
• src/common-preamble.tex: the shared package set, identical across courses.
• src/course.tex, everything specific to this course: title metadata, bullet and enumerate styles, hyperref, and the \input{sec/...} list. The house style plus colortbl provide \rowcolors, so the alternating-row shaded tables in the notes need no extra xcolor table option.
• sec/NN_*.tex: section files (the body of the notes), pulled in by course.tex via \coursebody.
• img/: figures (PNG screenshots and diagrams) included with \includegraphics.
• sna-notes.pdf: the compiled notes, in the folder root.
• No bibliography: the notes carry no .bib file and cite no sources.

Build

The notes use cleveref, which needs a final pass for cross-references, but no bibliography. Build from the folder root:

latexmk main.tex

latexmk runs pdflatex as many times as needed and writes the compiled PDF as sna-notes.pdf in the folder root. The LaTeX auxiliaries (.aux, .log, .toc, .bcf, .bbl, …) land in the root too and are git-ignored (listed in .gitignore). A .latexmkrc in the folder sets this up. To do it by hand instead:

pdflatex -jobname=sna-notes main && pdflatex -jobname=sna-notes main

(the second pass resolves the table of contents and cross-references). Requires a standard TeX Live installation. Alternatively, upload the folder to Overleaf (New Project → Upload Project), set main.tex as the main document, and compile.

Credits

Written by Francesco Secoli, revised with the help of Claude Code: the course slides and lectures were transcribed and refined into LaTeX, then reworked into standalone notes. Based on the Social Network Analysis course (a.y. 2024/25), University of Pisa. Contributions welcome: open an issue or a pull request.

Contents

The notes are ten sections, in reading order:

#	Section	Topics
1	Basic measures and models	Degree, paths, clustering, connected components; random (ER) networks and the configuration model; small-world phenomenon and Watts–Strogatz; scale-free networks and Barabási–Albert; model comparison
2	Centrality	Degree, eigenvector, PageRank, Katz; geometric centralities (closeness, harmonic, betweenness); homophily and assortative mixing, Newman's assortativity, clumpiness, multiscale mixing, conformity
3	Tie strength and resilience	Tie strength in real data, neighborhood overlap; network resilience, Molloy–Reed criterion, resilience of ER random graphs and scale-free networks under failure and attack
4	Simplicial complexes and hypergraphs	Higher-order interactions: simplicial complexes, hypergraphs and their incidence/projection representations, the s-analysis framework (s-walks, s-connectedness)
5	Community detection	Community definitions and evaluation rules (internal density, bridges, feature distance, percolation, entity closeness, link communities); external and internal evaluation strategies
6	Network dynamics	Temporal representations of dynamic networks and stability classes; stream graphs, temporal cliques/paths/components; random models for dynamic graphs, the activity-driven model
7	Link Prediction	Unsupervised prediction (neighborhood, path-based, ranking measures); supervised prediction and evaluation; interaction prediction in dynamic networks (community discovery, feature extraction, forecasting, classification)
8	Dynamic Community Detection (DCD)	Challenges: community smoothness, Theseus' ship paradox; taxonomy (instant-optimal, temporal trade-off, cross-time); evaluation with the RDyn benchmark and community-evolution patterns
9	Diffusion: decision-based models	Diffusion of innovations; collective action; cascades and threshold-based models; diminishing returns and influence maximization; herding. This section also runs into the epidemics material (compartmental and mean-field models, epidemics on networks, effective epidemic control), which currently sits under it with no heading of its own
10	Diffusion: opinion	Discrete- and continuous-opinion models; discrete versus continuous outcomes; polarisation and fragmentation in social media; the co-evolving voter model