week 01
1.01 Introduction to Network Science
Social Network Analysis
Historical Prospective
Complex Networks
- not regular, but not random
- non-trivial topology
- universal properties
- everywhere
- complex systems
Complex Networks
- power law node degree distribution: ”scale-free” networks
- small diameter and average path length: ”small world” networks
- hight clustering coefficient: transitivity
Power law
Power law
Power Law
Triads
- ”The Strength of Weak Ties”, Mark Grannoveter, 1973
- ”Spread of Information through a Population with Socio-Structural Bias. Assumption of Transitivity”, Anatol Rapoport, 1953
Triads
If A and B and B and C are strongly linked, the the tie between B and C is always present
Grannoveter, 1973
- strength of a tie
- high transitivity
- high clustering coefficient
High Clustering Coefficient
Stanley Milgram's experiment
Stanley Milgram's experiment
Stanley Milgram's experiment
- Reached the target N = 64(29%)
- Average chain length (L) = 5.2
- Channels:
- hometown (L) = 6.1
- business contacts (L) = 4.6
- from Boston (L) = 4.4
- from Nebraska (L) = 5.7
Stanley Milgram's experiment
- Email graph:
- D. Watts (2001), 48,000 senders, (L) ≈ 6
- MSN Messenger graph:
- J. Lescovec et al (2007), 240mln users, (L) ≈ 6.6
- Facebook graph:
- L. Backstrom et al (2012), 721 mln users, (L) ≈ 4.74
Spring of Neural Networks
Shallow embeddings
- DeepWalk: online learning of social representations, KDD 14, Cited by 10349, [pdf]
Complex Embeddings
- Semi-Supervised Classification with Graph Convolutional Networks, ICLR17, Cited by 30292, [pdf]
Transformers in graphs
- Graph Attention Networks, Cited by 8724, [pdf]
GraphRag
- From Local to Global: A Graph RAG Approach to Query-Focused Summarization, [pdf]
Conferences
Conferences
- Association for the Advancement of Artificial Intelligence AAAI
- Conference on Neural Information Processing Systems NeurIPS
- International Conference on Machine Learning ICML
- International Conference on Learning Representations ICLR
- Knowledge Discovery and Data Mining KDD
- International Conference on Data Mining ICDM
- Web Search and Data Mining WSDM
- International World Wide Web Conference WWW
- Learning on Graphs Conference LoG
Russian conferences
Literature
Most important articles
- Semi-Supervised Classification with Graph Convolutional Networks [pdf], [code], [video]
- Graph Attention Networks [pdf], [code]
- Inductive Representation Learning on Large Graphs [pdf], [code]
- Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering [pdf], [code]
- The Graph Neural Network Model [pdf]
Most important articles
- A Comprehensive Survey on Graph Neural Networks [pdf]
- Neural Message Passing for Quantum Chemistry [pdf]
- Spectral Networks and Locally Connected Networks on Graphs, ICLR14 [pdf] [video]
- How Powerful are Graph Neural Networks? [pdf]
- Convolutional Networks on Graphs for Learning Molecular Fingerprints [pdf], [code]
Books
- Network Science Book, Albert Barabasi
- ”Networks, Crowds, and Markets: Reasoning About a Highly Connected World”. David Easley and John Kleinberg, Cambridge University Press 2010.
- ”Networks: An Introduction”. Mark Newman. Oxford University Press, 2010.
- Graph Embeddings for Social Network Analysis: State of the Art. Paul Compagnon, Kilian Ollivier, 2019
- Advances in Network Clustering and Blockmodeling. Patrick Doreian, Vladimir Batagelj, Anǔska Ferligoj, 2020
Books
- Python for Graph and Network Analysis. Mohammed Zuhair Al-Taie, Seifedine Kadry, 2017
- Statistical mechanics of complex networks, R. Albert and A-L. Barabasi, Rev. Mod. Phys. 74, 47, 2002
- The Structure and Function of Complex Networks, M. E. J. Newman, SIAM Review, 45, pp 167-256, 2003
- Complex networks: Structure and dynamics, S. Boccaletti et al., Physics Reports, Volume 424, Issue 4-5, p. 175-308, 2006
Practical cases
Recommendation systems
Recommendation systems
Simulate physics with GNs
Learning to Simulate Complex Physics with Graph Networks [pdf]
Simulate physics with GNs
