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Network+Sciences-2010Spring-part-2

# Network+Sciences-2010Spring-part-2 - Network Sciences An...

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Network Sciences Lecturer: Prof. Xiang LI EE @ Fudan University 2010 Spring —— An English introductory course for undergraduate students Adaptive Networks and Control Lab

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Not fall in LOVE , but into NETWORKS Jacky Cheung e
Love & Networks ( J x + d & d & 7 d & J ( NK N K NK

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The Story Beginning
Long Long Ago

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Konigsberg, Konigsberg, East Prussia, 1800s
\$ even Bridges Puzzle Can one walk across the seven bridges and never cross the same one twice ?

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No one found such a route. Such efforts were finally given up in 1875 when the eighth bridge was built.
The Eighth bridge Google Earth, 2008

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Leonhard Euler (1707-1783) 1976/11/5 Swiss 10 Franc
Euler’s proof in 1736 The Seven-Bridge Konigsberg Puzzle has none answer!

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Euler’s approach Starting/end points: with odd number of edges; A “continuous” path which goes through all edges can have only one start and one end points; If a graph has more than 2 nodes with odd number of edges, such a path does not exist The first graph of human
Classroom Question Draw the new graph with the eighth bridge; Whether or not such a ‘eight-bridge’ puzzle have such a path? If yes, show one.

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Extension A salesman, N cities. Finding a path which starts from one city, and passes all cities only one time. If N>10, 100, 1000, how to find the path? CAN YOU? T ourist S alesman P roblem
Graph Theory L. Euler, Father of Graph Theory ( and of numerical analysis, of operations research,…… And, grandfather of sudoku ( Matrix Sudoku 8 ' Y * Æ E c T + 1-9 5 [ + / X ¡ Ø ……X¡Øﬂ ) For more interest, refer to: B. Bollobas, <Graph Theory: an introductory course>, Springer-Verlag, 1979 R. Diestel, <Graph Theory>, 3 rd edition, Springer- Verlag, 2006.

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SYNONYM Graph = Network Not only in this course, but also in this field.
Some Typical Regular Networks (a) All-to-all connected network (b) Ring-shaped network (c) Star-shaped network

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Give some examples in practice which may have such regular network topologies.
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