1. CS224w: Social and Information Network Analysis
Jure Leskovec, Stanford University

2. About the Class Introduce properties, models and tools for
Large real-world networks
Processes taking place in networks
through real applications and case studies
Goal: find patterns, rules, clusters, outliers, …
… in large static and evolving graphs
… in processes spreading over the networks
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

3. ******************
Faster and (less complex systems) more Web and Social Networks based motivation
Example pictures from NetInf
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

4. Networks & Complex Systems
We are surrounded by hopelessly complex systems:
Society is a collection of six billion individuals
Communication systems link electronic devices
Information and knowledge is organized and linked
Thousands of genes in our cells work together in a seamless fashion
Our thoughts are hidden in the connections between billions of neurons in our brain
These systems, random looking at first, display signatures of order and self-organization
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

5. Networks
Each such system can be represented as a network, that defines the interactions between the components
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

6. Networks: Communication
Graph of the Internet (Autonomous Systems)
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

7. Networks: Information
Connections between political blogs
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

8. Seven Bridges of Königsberg (Euler 1735)
Networks: Technology
Seven Bridges of Königsberg (Euler 1735)
Return to the starting point by traveling each link of the graph once and only once.
London Underground
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

9. Networks: Organizations
: departments
: consultants
: external experts
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

10. Networks: Economy Nodes: Links: Bio-tech companies, 1991 Companies
Investment
Pharma
Research Labs
Public
Biotechnology
Links:
Collaborations
Financial
R&D
Bio-tech companies, 1991
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

11. Human brain has between 10-100 billion neurons
Networks: Brain
Human brain has between billion neurons
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

12. Protein-Protein Interaction Networks:
Networks: Cells
Protein-Protein Interaction Networks:
Nodes: Proteins
Edges: ‘physical’ interactoins
Metabolic networks:
Nodes: Metabolites and enzymes Edges: Chemical reactions
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

13. Why Networks?
Behind each such system there is an intricate wiring diagram, a network, that defines the interactions between the components
We will never understand a complex system unless we understand the networks behind it
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

14. Reasoning about Networks
How do we reason about networks
Empirical: Study network data to find organizational principles
Mathematical models: Probabilistic, graph theory
Algorithms for analyzing graphs
What do we hope to achieve from models of networks?
Patterns and statistical properties of network data
Design principles and models
Understand why networks are organized the way they are (Predict behavior of networked systems)
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

15. Networks: Structure & Process
What do we study in networks?
Structure and evolution:
What is the structure of a network?
Why and how did it became to have such structure?
Processes and dynamics:
Networks provide “skeleton” for spreading of information, behavior, diseases
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

16. Age and size of networks
Networks: Why Now?
Age and size of networks
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

17. Networks: Why Now?
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

18. Networks: Why Now?
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

19. Why Networks? Why Now? Why is the role of networks expanding?
Data availability
Rise of the Web 2.0 and Social media
Universality
Networks from various domains of science, nature, and technology are more similar than one would expect
Shared vocabulary between fields
Computer Science, Social science, Physics, Economics, Statistics, Biology
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

20. Networks: Impact
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

21. Networks: Impact Intelligence and fighting (cyber) terrorism 9/19/2018
Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

22. Networks: Impact Predicting epidemics Real Predicted 9/19/2018
Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

23. Networks: Impact Interactions of human disease Drug design 9/19/2018
Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

24. Networks Really Matter
Use more WEB/SOCIAL examples, less complex systems
If you were to understand the spread of diseases, can you do it without networks?
If you were to understand the WWW structure and information, hopeless without invoking the Web’s topology.
If you want to understand human diseases, it is hopeless without considering the wiring diagram of the cell.
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

25. Course Logistics

26. Course Syllabus
Covers a wide range of network analysis techniques – from basic to state-of-the-art
You will learn about things you heard about:
Six degrees of separation, small-world, page rank, network effects, P2P networks, network evolution, spectral graph theory, virus propagation, link prediction, power-laws, scale free networks, core-periphery, network communities, hubs and authorities, bipartite cores, information cascades, influence maximization, …
Covers algorithms, theory and applications
It’s going to be fun 
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

27. Prerequisites Good background in: Programming: 4 recitation sessions:
Algorithms
Graph theory
Probability and Statistics
Linear algebra
Programming:
You should be able to write non-trivial programs
4 recitation sessions:
2 to review basic mathematical concepts
2 to review programming tools (SNAP, NetworkX)
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

28. Logistics Course website: http://cs224w.stanford.edu
Slides posted at least 30 min before the class
Required readings:
Mostly chapters from Easley&Kleinberg book
Papers
Optional readings:
Papers and pointers to additional literature
This will be very useful for reaction paper and project proposal
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

29. Text Books Recommended textbook: Optional books:
D. Easley, J. Kleinberg: Networks, Crowds, and Markets: Reasoning About a Highly Connected World
Freely available at:
Optional books:
Matthew Jackson: Social and Economic Networks
Mark Newman: Networks: An introduction
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

30. Work for the Course Assignment Due on Homework 1 October 13
Reaction paper
October 20
Project proposal
October 27
Homework 2
November 3
Competition
November 10
Project milestone
November 17
Project write-up
December 11 (no late days!)
Project poster presentation
December 16 12:15-3;15pm
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

31. Grading Final grade will be composed of: 2 homeworks: 15% each
Reaction paper: 10%
Substantial class project: 60%
Proposal: 15%
Project milestone: 15%
Final report: 60%
Poster session: 10%
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

32. Homeworks, Write-ups, Reports
Assignments (homeworks, write-ups, reports) take time. Start early!
How to submit?
Paper: Box outside the class and in Gates basement
We will grade on paper!
You should also submit electronic copy:
1 PDF/ZIP file (writeups, experimental results, code)
Submission website:
SCPD: Only submit electronic copy & send us
7 late days for the quarter:
Max 4 late days per assignment
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

33. Course Projects Substantial course project:
Where do they get the data?
What code/machines they use?
Substantial course project:
Experimental evaluation of algorithms and models on an interesting network dataset
A theoretical project that considers a model, an algorithm and derives a rigorous result about it
An in-depth critical survey of one of the course topics and offering a novel perspective on the area
Performed in groups of (exactly) 3 students
Project is the main work for the class
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

34. Course Assistants Office hours schedule!!! Borja Peleato (head TA)
Chenguang Zhu
Evan Rosen
Dakan Wang
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

35. Communication Piazza Q&A website:
If you don’t address, send us and we will register you to Piazza
For ing course staff, always use:
For course announcements subscribe to:
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

36. Sitting-in & Auditing You are welcome to sit-in and audit the class
Please send us saying that you will be auditing the class
To receive announcements, subscribe to the mailing list:
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

37. Starter Topic: Structure of Networks

38. Structure of Networks?
Network is a collection of objects where some pairs of objects are connected by links What is the structure of the network?
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

39. Components of a Network
Objects: nodes, vertices N
Interactions: links, edges E
System: network, graph G(N,E)
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

40. Networks or Graphs? Network often refers to real systems
Web, Social network, Metabolic network
Language: Network, node, link
Graph: mathematical representation of a network
Web graph, Social graph (a Facebook term)
Language: Graph, vertex, edge
We will try to make this distinction whenever it is appropriate, but in most cases we will use the two terms interchangeably
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

41. Networks: Common Language
Movie 1
Movie 3
Movie 2
Actor 3
Actor 1
Actor 2
Actor 4
Peter
Mary
Albert
co-worker
friend
brothers
Protein 1
Protein 2
Protein 5
Protein 9
|N|=4
|E|=4
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

42. Choosing Proper Representation
Choice of the proper network representation determines our ability to use networks successfully:
In some cases there is a unique, unambiguous representation
In other cases, the representation is by no means unique
The way you assign links will determine the nature of the question you can study
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

43. Choosing Proper Representation
If you connect individuals that work with each other, you will explore a professional network
If you connect those that have a sexual relationship, you will be exploring sexual networks
If you connect scientific papers that cite each other, you will be studying the citation network
If you connect all papers with the same word in the title, you will be exploring what? It is a network, nevertheless
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

44. Undirected vs. Directed Networks
Links: undirected (symmetrical)
Undirected links:
Collaborations
Friendship on Facebook
Directed
Links: directed (arcs)
Directed links:
Phone calls
Following on Twitter A B D C L M F G H I D B C E G A F
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

45. Connectivity of Graphs
Connected (undirected) graph:
Any two vertices can be joined by a path.
A disconnected graph is made up by two or more connected components D C A B F G D C A B F G
Largest Component:
Giant Component
Isolated node (F)
Bridge edge: If we erase it, the graph becomes disconnected.
Articulation point: If we erase it, the graph becomes disconnected.
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

46. Connectivity of Directed Graphs
Strongly connected directed graph
has a path from each node to every other node and vice versa (e.g., A-B path and B-A path)
Weakly connected directed graph
is connected if we disregard the edge directions E F B A
Graph on the left is connected but not strongly connected. D C G
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

47. Web as a Graph Q: What does Web “look like” at a global level?
Explain what we will do:
-- take a real system
-- represent it as a graph
-- use language of graph theory to reason about the shape of the web
-- do a computational experiment
-- learn something about the structure of the web
Q: What does Web “look like” at a global level?
Web as a graph:
Nodes = pages
Edges = hyperlinks
What is a node?
Problems:
Dynamic pages created on the fly
“dark matter” – inaccessible database generated pages
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

48. The Web as a Graph I teach a class on Networks.
CS224W: Classes are in the Computer Science building
Computer Science Department at Stanford
Stanford University
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

49. The Web as a Graph In early days of the Web links were navigational
I teach a class on Networks.
CS224W: Classes are in the Computer Science building
Computer Science Department at Stanford
Stanford University
In early days of the Web links were navigational
Today many links are transactional
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

50. The Web as a Directed Graph
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

51. Other Information Networks
Citations
References in an Encyclopedia
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

52. How Does the Web Look Like?
How is the Web linked?
What is the “map” of the Web?
Web as a directed graph [Broder et al. 2000]:
Given node v, what can v reach?
What other nodes can reach v? E C A B G F D
In(A) = {A,B,C,E,G}
Out(A)={A,B,C,D,F}
In(v) = {w | w can reach v} Out(v) = {w | v can reach w}
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

53. Directed Graphs Two types of directed graphs:
Strongly connected:
Any node can reach any node via a directed path
In(A)=Out(A)={A,B,C,D,E}
DAG – Directed Acyclic Graph:
Has no cycles: if u can reach v, then v can not reach u
Any directed graph can be expressed in terms of these two types E C A B D E C A B D
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

54. Strongly Connected Component
Strongly connected component (SCC) is a set of nodes S so that:
Every pair of nodes in S can reach each other
There is no larger set containing S with this property E F B A
Strongly connected components of the graph: {A,B,C,G}, {D}, {E}, {F} D C G
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

55. Strongly Connected Component
Fact: Every directed graph is a DAG on its SCCs
(1) SCCs partitions the nodes of G
Each node is in exactly one SCC
(2) If we build a graph G’ whose nodes are SCCs, and with an edge between nodes of G’ if there is an edge between corresponding SCCs in G, then G’ is a DAG
Strongly connected components of graph G: {A,B,C,G}, {D}, {E}, {F}
G’ is a DAG: E F B G
{E} A
{F} D C G
{A,B,C,G} G’
{D}
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

56. Proof Why is (2) true? G’ (graph of SCCs) is a DAG
Expand 2 slides: be more explicit about the proof by contradiction. Spell it out.
Why is (1) true? SCCs partitions the nodes of G.
Suppose node v is a member of 2 SCCs S and S’.
Then SS’ is one large SCC:
Why is (2) true? G’ (graph of SCCs) is a DAG
If G’ is not a DAG, then we have a directed cycle.
Now all nodes on the cycle are mutually reachable, and all are part of the same SCC. v S S’ G’
{E}
{F}
{A,B,C,G}
{D}
Now {A,B,C,G,E,F} is a SCC
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

57. Graph Structure of the Web
Picture, animation of the BFS
Picture why the intersection of In and Out is SCC
Goal: Take a large snapshot of the Web and try to understand how it’s SCCs “fit together” as a DAG
Computational issue:
Want to find a SCC containing node v?
Observation:
Out(v) … nodes that can be reached from v
SCC containing v is: Out(v) ∩ In(v)
= Out(v,G) ∩ Out(v,G), where G is G with all edge directions flipped v
Out(v)
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

58. Graph Structure of the Web
There is a giant SCC
There won’t be 2 giant SCCs:
It just takes 1 page from one SCC to link to the other SCC
If the components have millions of pages the likelihood of this not happening is very small
Giant SCC1
Giant SCC2
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

59. Bow-tie Structure of the Web
Give better explanation of how can we conclude the bowtie structure
250 million pages, 1.5 billion links [Broder et al. 2000]
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis

60. What did We Learn/Not Learn ?
Just managed to finish the lecture.
Need to kill a few slides in the intro to save time
Learn:
Some conceptual organization of the Web (i.e., the bowtie)
Not learn:
Treats all pages as equal
Google’s homepage == my homepage
What are the most important pages
How many pages have k in-links as a function of k?
The degree distribution: ~ 1 / k2
Link analysis ranking -- as done by search engines (PageRank)
Internal structure inside giant SCC
Clusters, implicit communities?
How far apart are nodes in the giant SCC:
Distance = # of edges in shortest path
Avg = 16 [Broder et al.]
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Jure Leskovec, Stanford CS224W: Social and Information Network Analysis