Mathematics and Social Networks
Transcript of Mathematics and Social Networks
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Mathematics and Social Networks
Mason A. Porter (applied mathematics tutor)
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What is a network? A network consists of nodes representing entities. Nodes are connected by edges representing ties between the entities.
Examples:
Individuals connected by Facebook “friendships”.
Web pages connected by hyperlinks.
Contiguous cities on a train route.
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Networks are Everywhere
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“When we understand this slide, we’ll have won the war.”
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More Brains
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Types of Networks
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Representing a Network
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Goals of “Network Science”
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Basic Principles
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Small Worlds 6 degrees of separation (psychologist Stanley Milgram)
6 degrees of Kevin Bacon
Erdös numbers
Mathematical models developed starting in late 1990s to study this (starting with Watts & Strogatz, 1998)
How to navigate small worlds?
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One way to try to understand the large-scale structure of networks is to group nodes into “communities” in which the nodes have a lot of ties
among themselves (e.g. students in Somerville College)
Finding such groupings require the development of computer algorithms, which is one of the things that my students and I study.
Facebook Friendship Networks
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Facebook Networks
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Develop and use computer algorithms to group circles of friends in an automated fashion.
The problem is both very difficult and very interesting.
Detecting Communities
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There are equations.
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Princeton: Class Year & Major
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Quantitative Comparisons
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How do universities organize?
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What do you think?
What does this tell us about
how Facebook works?
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Student project by Yulian Ng (Somerville, 4th year, Mathematics)
I have advised many undergraduate research projects in networks, and there will be many more in the future. So this opportunity
awaits you if you come here.
Application to Epidemics
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Application to Finance
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Some exchange rates changed roles in the network right when the Credit Crunch began!
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One can also study things like voting networks, such as voting on resolutions in the United Nations General Assembly.
Voting Networks
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Configuration of Human Brain Networks During Learning
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[email protected] Questions?