复旦大学：《网络科学导论 Introduction to Network Science》教学课件_2- Classic Network Concepts & Properties

Network science An English introductory course for undergraduate students Lecturer: Dr. Cong LI ee@ Fudan University Adaptive Networks and Control Lab

Network Science Lecturer: Dr. Cong LI EE @ Fudan University —— An English introductory course for undergraduate students Adaptive Networks and Control Lab

ARE you Are READy? You Ready? Are You ready? Experiene www.experiencecj.com Are yourureac E左 ARE YOU READY? Sawyer is, and he 'll be back tomorrow

Are You Ready?

Ready Fall

Ready…… Fall……

Long Long ago

Long Long Ago

Konigsberg east Prussia, 1700s

Konigsberg, East Prussia, 1700s

X Seven Bridges Puzzle Can one walk across the seven bridges and never cross the same one twice No one found such a route 需图确

Seven Bridges Puzzle • Can one walk across the seven bridges and never cross the same one twice ? No one found such a route

Leonhard Euler (1707-1783) 28N lesar 1976/11/5 Swiss 10 franc

Leonhard Euler (1707-1783) 1976/11/5 Swiss 10 Franc

Euler’ s proof in1736 The Seven-Bridge Konigsberg Puzzle has none answer Fe 所明 AnSWer T-5

Euler’s proof in 1736 • The Seven-Bridge Konigsberg Puzzle has none answer!

数图 Euler’ s approach Starting/end points with odd EsFr number of eages a continuous path which goes through all edges can have only one start and one end points, D If a graph has more than 2 nodes with odd number of edges such a path does not B exist he first graph of human

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

More hints from euler A suitable mapping approach from a (networking) system to a network(graph) The key-point is the definitions on nodes and edges How to find a suitable solution of a difficult problem

More hints from Euler • A suitable mapping approach from a (networking) system to a network (graph). • The key-point is the definitions on nodes and edges. • How to find a suitable solution of a difficult problem