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The Science of Networks 1.1 Welcome! CompSci 96: The Science of Networks SocSci 119 M,W 1:15-2:30 Professor: Jeffrey Forbes

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Presentation on theme: "The Science of Networks 1.1 Welcome! CompSci 96: The Science of Networks SocSci 119 M,W 1:15-2:30 Professor: Jeffrey Forbes"— Presentation transcript:

1 The Science of Networks 1.1 Welcome! CompSci 96: The Science of Networks SocSci 119 M,W 1:15-2:30 Professor: Jeffrey Forbes http://www.cs.duke.edu/courses/spring11/cps096

2 The Science of Networks 1.2 Today’s topics l What is a network? Why are they important? l The Oracle of Bacon l Network construction l Acknowledgements  Notes taken from Michael Kearns,Lada Adamic, and Nicole Immorlica l Upcoming  Network Structure: Graph Theory  GUESS

3 The Science of Networks 1.3 Course Information l Grading Breakdown l No background assumed, but we will  Interpret and work with models both quantitatively and qualitatively l Important Dates  Midterm 2/23  Projects due 4/21  Final 5/5 9am-Noon l Let me know ASAP if you have any concerns “The structure and interconnectivity of social, technological, and natural networks. Network structure: graph theory, economic, social, physical, and natural networks. Network behavior: game theory, markets and strategic interaction, aggregate and emergent functions, and dynamics. Information networks: search and integration. Applications in sociology, economics, public policy, and computing..” AssessmentWeight (approx) Assignments (5)30% Blog Posts (3)15% Classwork/Com munity 15% Midterm15% Final25%

4 The Science of Networks 1.4 A Future for Computer Science?

5 The Science of Networks 1.5 Emerging science of networks l Examining apparent similarities between many human and technological systems & organizations  Importance of network effects in such systems l How things are connected matters greatly  Structure, asymmetry and heterogeneity l Details of interaction matter greatly  The metaphor of viral spread  Dynamics of economic and strategic interaction  Qualitative and quantitative; can be very subtle l A revolution of  measurement  theory  breadth of vision (M. Kearns)

6 The Science of Networks 1.6 What is a network? l A collection of individual or atomic entities l Links can represent any pairwise relationship  Links can be directed or undirected l Network: entire collection of nodes and links  might sometimes be annotated by other info (weights, etc.) l For us, a network is an abstract object (list of pairs) and is separate from its visual layout  that is, we will be interested in properties that are layout- invariant l We will be interested in properties of networks  often structural properties  often statistical properties of families of networks

7 The Science of Networks 1.7 Repesenting networks l Networks are collections of points joined by lines. l What kinds of questions might we ask? “Network” ≡ “Graph” pointslines verticesedges, arcsmath nodeslinkscomputer science sitesbondsphysics actorsties, relationssociology node edge

8 The Science of Networks 1.8 Definitions l Path: a sequence of nodes (v 1, …, v k ) such that for any adjacent pair v i and v i+1, there’s an edge e i,i+1 between them. l Distance: the length of the shortest path between two nodes l Diameter: the maximum shortest-path distance between any two nodes 28374561

9 The Science of Networks 1.9 Network Definitions l Network size: total number of vertices (denoted n )  Maximum possible number of edges ( m )? l If the distance between all pairs is finite, we say the network is connected ; else it has multiple components l Attributes of edges  Weight or cost  Direction l Degree of a node v = number of edges connected to v  Directed versions (in-degree and out-degree) l What else might we want to model beyond just the connections?

10 The Science of Networks 1.10 Issues l Why model networks? Structure & dynamics  Models (structure): who is linked to whom? How does position within a network (dis)advantage an agent? What are the factors that lead people to trust each other? Graph theoretic models  Implications (dynamics): individual behavior can have global consequences Diffusion of disease and information Search by navigating the network Resilience Population, structural, and aggregate effects Game theoretic models

11 The Science of Networks 1.11 Social networks l Example: Acquaintanceship networks  vertices: people in the world  links: have met in person and know last names  hard to measure l Example: scientific collaboration  vertices: math and computer science researchers  links: between coauthors on a published paper  Erdos numbers : distance to Paul Erdos  Erdos was definitely a hub or connector; had 507 coauthors l How do we navigate in such networks?

12 The Science of Networks 1.12 Acquaintanceship & more

13 The Science of Networks 1.13 Six Degrees of Bacon l Background  Stanley Milgram’s Six Degrees of Separation?  Craig Fass, Mike Ginelli, and Brian Turtle invented it as a drinking game at Albright College  Brett Tjaden, Glenn Wasson, Patrick Reynolds have run t online website from UVa and beyond  Instance of Small-World phenomenon l http://oracleofbacon.org handles 2 kinds of requests 1. Find the links from Actor A to Actor B. 2. How good a center is a given actor?  How does it answer these requests?

14 The Science of Networks 1.14 How does the Oracle work? l Not using Oracle™ l Queries require traversal of the graph BN = 0 Mystic River Apollo 13 Footloose John Lithgow Sarah Jessica Parker Bill Paxton Tom Hanks Sean Penn Tim Robbins BN = 1 Kevin Bacon

15 The Science of Networks 1.15 How does the Oracle Work? Kevin Bacon Mystic River Apollo 13 Footloose John Lithgow Sarah Jessica Parker Bill Paxton Tom Hanks Sean Penn Tim Robbins BN = 0 BN = 1 Sweet and Lowdown Fast Times at Ridgemont High War of the Worlds The Shawshank Redemption Cast Away Forrest Gump Tombstone A Simple Plan Morgan Freeman Sally Field Helen Hunt Val Kilmer Miranda Otto Judge Reinhold Woody Allen Billy Bob Thornton BN = 2 l BN = Bacon Number l Queries require traversal of the graph

16 The Science of Networks 1.16 How does the Oracle work? Mystic River Footloose John Lithgow Sarah Jessica Parker Tom Hanks Sean Penn Tim Robbins BN = 0 BN = 1 Sweet and Lowdown Fast Times at Ridgemont High War of the Worlds The Shawshank Redemption Cast Away Forrest Gump A Simple Plan Morgan Freeman Sally Field Helen Hunt Miranda Otto Judge Reinhold Woody Allen Billy Bob Thornton BN = 2 Bill Paxton Tombstone Val Kilmer Apollo 13 Kevin Bacon l How do we choose which movie or actor to explore next? l Queries require traversal of the graph

17 The Science of Networks 1.17 Center of the Hollywood Universe? l 1,246,221 people can be connected to Bacon l Is he the center of the Hollywood Universe?  Who is?  Who are other good centers?  What makes them good centers? l Centrality  Closeness: the inverse average distance of a node to all other nodes  Degree: the degree of a node  Betweenness: a measure of how much a vertex is between other nodes

18 The Science of Networks 1.18 Oracle of Bacon l Name someone who is 4 degrees or more away from Kevin Bacon 14 25 36 l What characteristics makes someone farther away? l What makes someone a good center? Is Kevin Bacon a good center?

19 The Science of Networks 1.19 Sample Blog Post l I'm Related to Kevin Bacon?  Overview of the Oracle of Bacon:In class we have talked a lot about social and computer networks and all of their component parts. We have learned many important aspects of networks and what makes them operate. One of the most interesting and complex notions is that of centrality and how one can go about calculating centrality within a social network. The Oracle of Bacon is one of the best examples of a project that has created an elaborate social network around the central figure of Kevin Bacon. However, it is interesting that the site proves Kevin Bacon to actually not be the center of the Hollywood network, in fact there are actually 1,048 actors who would make better centers than Bacon. Here is a breakdown of the best and worst centers of the Hollywood network. Although the only other actor mentioned who would make a better center is Sean Connery, it can be speculated as to what makes a great center. A good center would have to be an older actor, have appeared in many movies and many varities of movies, have appeared in large productions with many actors and have worked overseas. Alternatively, a bad center would be young, have appeared in only one type of movie, or one movie in general!The Oracle of BaconHere

20 The Science of Networks 1.20  Why is the Oracle of Bacon Interesting to us? In reality, the game is an example of the small world phenomenon. The small world phenomenon was researched by Stanley Milgram as he examined the average path length for social networks of people in the United States. The phenomenon shows that paths between nodes are always shorter than expected, which is proved in the game. This oracle of Bacon game was designed by computer scientists at the University of Virginia in order to create an engaging way of dealing with the small world phenomenon. The program for calculating a Bacon number was developed by mapping networks from http://imdb.com/ (the database for movies and actors information).Stanley Milgramhttp://imdb.com/  Other related points Here is the original paper by Stanley Milgram, upon which all of this information is based. The game works to find links between different actors and find the degree of separation from Bacon. It is amazing that almost any actor, no matter how obscure, can be linked to Bacon within six degrees and the average is under three links (2.960). Here It is also interesting to look at the earlier examples of small world phenomenon, which inspired the oracle of Bacon. Erdos numbers refer to the number of nodes mathematicians are away from Paul Erdos, a Hungarian mathematician famous for collaboration. The Erdos number project gives details similar to the Oracle of Bacon about the amount of connectivity within the network of mathematicians. In this network the median Erdos number is 5; the mean is 4.65, and the standard deviation is 1.21. This shows that there is slightly less connectivity, but a high degree of centrality.Erdos number project

21 The Science of Networks 1.21  Here is a visualization of the Erdos Network.  More recent centrality work There are many examples of computer scientists who have dealt with the six degrees theory in their analysis of the small-world phenomenon including Jon Kleinberg. His paper: Could it be a Big World After All? The `Six Degrees of Separation’ Myth. Society, April 2002 deals with a lot of the important ideas discussed above. Kleinberg argues that the initial data used to create the notion of the small-world phenomenon was actually skewed and data shows that there might actually be less connectivity between people that was previously believed. This paper was published in 2002, and it does not seem to have garnered a large amount of debate amongst the scholarly community. It seems that more work and experimentation needs to be done in this field to in attempt to make claims about the connectedness of the actual world. Although Kleinberg and others made some really interesting points initially, unfortunately the computer science world seems focused on novelty, not finishing work on a phenomenon, so it may be awhile before all of our questions are answered!paper

22 The Science of Networks 1.22 Physical Networks l The Internet  Vertices: Routers  Edges: Physical connections l Another layer of abstraction  Vertices: Autonomous systems  Edges: peering agreements  Both a physical and business network l Other examples  US Power Grid  Interdependence and August 2003 blackout

23 The Science of Networks 1.23 What does the Internet look like?

24 The Science of Networks 1.24 US Power Grid

25 The Science of Networks 1.25 Business & Economic Networks l Example: eBay bidding  vertices: eBay users  links: represent bidder-seller or buyer-seller  fraud detection: bidding rings l Example: corporate boards  vertices: corporations  links: between companies that share a board member l Example: corporate partnerships  vertices: corporations  links: represent formal joint ventures l Example: goods exchange networks  vertices: buyers and sellers of commodities  links: represent “permissible” transactions

26 The Science of Networks 1.26 Enron

27 The Science of Networks 1.27 Content Networks l Example: Document similarity  Vertices: documents on web  Edges: Weights defined by similarity  See TouchGraph GoogleBrowser l Conceptual network: thesaurus  Vertices: words  Edges: synonym relationships

28 The Science of Networks 1.28 Wordnet Source: http://wordnet.princeton.edu/man/wnlicens.7WN

29 The Science of Networks 1.29 Biological Networks l Example: the human brain  Vertices: neuronal cells  Edges: axons connecting cells  links carry action potentials  computation: threshold behavior  N ~ 100 billion

30 The Science of Networks 1.30 Gene regulatory networks l Humans have only 30,000 genes, 98% shared with chimps l The complexity is in the interaction of genes l Can we predict what result of the inhibition of one gene will be? Source: http://www.zaik.uni-koeln.de/bioinformatik/regulatorynets.html.en

31 The Science of Networks 1.31 Types of networks l Pick a class of network: l Give a real-world example of such a network:  What are the vertices (nodes)?  What are the edges (links)?  How is the network formed? Is it decentralized or centralized? Is the communication or interaction local or global?  What is the network's topology? For example, is it connected? What is its size? What is the degree distribution?

32 The Science of Networks 1.32 Graph properties l Max Degree? l Center?

33 The Science of Networks 1.33 Wrap up l Networks are everywhere and can be used to describe many, many systems. l By modeling networks, we can start to understand their properties and the implications those properties have for processes occurring on the network


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