L_structnets.sp11 - CS 525 Advanced Distributed Systems...

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1 CS 525 Advanced Distributed Systems Spring 2011 Indranil Gupta (Indy) Structure of Networks April 28, 2011 All Slides © IG
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2 1981
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3 1981 Countries= nodes Treaties= edges Graph or Network
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4 1992
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5 The Internet (Internet Mapping Project, color coded by ISPs) PCs= nodes Connected= edges
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6 Food Web of Little Rock Lake,WI Electric Power Grid Metabolic reaction network
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7 This Lecture: Common Thread Networks Structure of, Dynamics within, We’ll study networks at three different “levels”
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8 Lowermost Level: Basics, Physical Phenomena, and Life
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9 Complexity of Networks Structural: human population has ~7 B nodes, there are millions of computers on the Internet… Evolution: people make new friends all the time, ISP’s change hands all the time… Diversity: some people are more popular, some friendships are more important… Node Complexity: PCs have different CPUs, Windows is a complicated OS… Emergent phenomena: simple end behavior complex system-wide behavior. If we understand the basics of climate change, why is the weather so unpredictable?
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10 1. Network Structure “Six degrees of Kevin Bacon” Milgram’s experiment in 1970 Watts and Strogatz Model Kleinberg’s algorithmic results Recent work on mapping Internet, WWW, p2p overlays, electric power grid, protein networks, co-authorship among scientists These networks have “evolved naturally”
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11 Ring graph Fully Connected graph Random graph Power Law Graph (Degenerate: tree)
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12 A Scientist’s Perspective Two important metrics Clustering Coefficient: CC Pr(A-B edge, given an A-C edge and a C-B edge) Path Length of shortest path Ring graph: high CC, long paths Random graph: low CC, short paths Small World Networks: high CC, short paths
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13 Ring graph Random Graph Clustering Coefficient Path Length Small World Networks Convert more and more edges to point to random nodes
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14 Most “natural evolved” networks are (probably) small world Network of actors six degrees of Kevin Bacon Network of humans Milgram’s experiment Co-authorship network “Erdos Number” Many of these networks also “grow incrementally” [Faloutsos and Faloutsos]
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15 Another Scientific Viewpoint That was about “nature of neighbors”; what about number of neighbors? Degree distribution – what is the probability of a given node having k edges (neighbors, friends, …) Regular graph: all nodes same degree Gaussian Random graph: Exponential Power law : α - k c k e . -
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16 l o g ( n u m b e r f d s ) log (node degree= k ) Basics: The Log-Log Plot Power law Exponential Heavy tailed 1 10 100 1000 1 0 Number of nodes with degree k is ~ α - k
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17 WWW is a power law graph NCSTRL co-author graph is power law, with exponential cutoff Electric Power Grid graph is exponential Social network of Utah Mormons is Gaussian 4 . 2 1 . 2 - = α
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This note was uploaded on 12/08/2011 for the course CS 525 taught by Professor Gupta during the Spring '08 term at University of Illinois, Urbana Champaign.

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L_structnets.sp11 - CS 525 Advanced Distributed Systems...

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