复旦大学：《网络科学导论 Introduction to Network Science》教学课件_3- Erdos Ranyi random graphs

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

Network definition a graph g(n, L(network topology) specifies how items called nodes are interconnected or related to other nodes y links Star rIng Complete graph L=N-1 L=N L=N(N-1)/2

Network Definition A graph G(N, L) (network topology) specifies how items, called nodes, are interconnected or related to other nodes by links. L = N-1 ring L = N Complete graph L = N(N-1)/2 Star

But, is everything including a network none of uncertainty? FRANK ARE YoU SURE IT WONT EXPLODE Frank are you sure cE③度价 OCRA&立 it won't explode SPi

But, is everything including a network none of uncertainty? Frank, are you sure it won’t explode?

QUANTUM COPS The Uncertainty Principality- Heisenberg you have any idea how fast were going back there? Uncertainty Principle the values of certain pairs of conjugate variables(position and momentum, for instance)cannot both be known with arbitrary ICH. YOURE SJT 605. N A GNeN WORLD HOW CAN WE BE SURE precision. That is, the more precisely one variable is known the less precisely the other is known

Heisenberg Uncertainty Principle • the values of certain pairs of conjugate variables (position and momentum, for instance) cannot both be known with arbitrary precision. That is, the more precisely one variable is known, the less precisely the other is known

How to improve the precision Ockham's razor: entities should not be multiplied unnecessarily M SIMPLE JUST ONE BL IPDI Principle: Increasing OCCAM'S RAZOR! Precision with Decreasing Intelligence

How to improve the precision? • Ockham's Razor: Entities should not be multiplied unnecessarily • IPDI Principle: Increasing Precision with Decreasing Intelligence

万年太久,只争朝夕 《满江红》,毛泽东,1963 系北包级场g的着有: 劣红 和这含森 1

一万年太久，只争朝夕 ——《满江红》，毛泽东，1963

SYNONYM in this course Uncertainty= Randomness

SYNONYM in this course • Uncertainty = Randomness

a graph with uncertainty 1736, Euler, the first graph(without uncertainty) A+ 1959, Erdos and Renyi, the first graph with uncertainty, the first network model to describe complexity

A graph with uncertainty? • 1736, Euler, the first graph (without uncertainty) • 1959, Erdos and Renyi, the first graph with uncertainty, the first network model to describe complexity

Random graph Theory Erdos- Renyi model Erdos-Renyi (Publ. Math. Inst. Hung. Acd. Sci. 5,17 (1960) Paul erdos Alfred Reny N nodes. each pair of nodes are connected with p=0.2 ER probability p

Random Graph Theory Erdös – Rényi model Paul Erdös Alfred Rényi

One main interest of the random graph theory is to find in what connection probability p, a particular property of a graph will most likely arise. b)p=0.1 (c)p=0.15 (d)p=0.25

• One main interest of the random graph theory is to find in what connection probability p, a particular property of a graph will most likely arise