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contagion10

# contagion10 - Contagion Tipping and Navigation in Networks...

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Contagion, Tipping and Navigation in Networks Networked Life CIS 112 Spring 2010 Prof. Michael Kearns

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What is a Network? A c o lle c tio n o f  individual  or  atomic  entities Referred to as  nodes  or  vertices  (the “dots” or “points”) Collection of  links  or  edges  between vertices (the “lines”) Links can represent any  pairwise relationship Links can be  directed  or  undirected Network: entire collection of nodes and links might sometimes be annotated by other info (weights, etc.) 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 Extremely general, but not everything: e.g. menage a trois may lose information by pairwise representation We will be interested in  properties  of networks often  structural  properties often  statistical  properties of  families  of networks
Some Terminology Network  size:  total number of vertices (denoted N) Maximum possible number of edges: N(N-1)/2 ~ N^2/2 (>> N) Distance  between vertices u and v: number of edges on the  shortest  path from u to v can consider directed or undirected cases infinite if there is no path from u to v Diameter  of a network: worst-case  diameter: largest distance between a pair average-case  diameter: average distance If the distance between all pairs is finite, we say the network is  connected;  else it has multiple  components Degree  of vertex v: number of edges connected to v

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Illustrating the Concepts 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 MK’s Erdos number is 3, via Kearns   Mansour   Alon   Erdos how do we  navigate  in such networks? Example: “real-world” acquaintanceship networks vertices: people in the world links: have met in person and know last names hard to measure let’s examine the results of our own  last-names exercise
average = 31.3, std = 22.0 min = 2 max = 101 Chester Chen Danielle Greenberg Allison Mishkin James Katz

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# of individuals # of last names known average = 26.6 min = 2 max = 114 Jason Chou Gaoxiang Hu
# of last names known # of individuals average = 30.7 min = 0 max = 113 Geoffrey Kiderman Nechemya Kagedan

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Structure, Dynamics, and Formation
Network Structure (Statics) Em phas ize  pure ly  structural  properties size, diameter, connectivity, degree distribution, etc.

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contagion10 - Contagion Tipping and Navigation in Networks...

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