Introduction

C. Kim2016

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Networks General definition

– A system to transfer entities– Consists of nodes and links

Communication network– To move information– Node: routers, switches, servers, hosts, …– Link: wired or wireless connection

Social network– Represent relationships/interactions between person,

organizations, info, …– Node (Object)– Edge: relations, interactions, like/dislike, refer, collaboration,

follow, …

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Social Network – Example1

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HomophilySelection or Social influence?

Political blogs

Why Social Networks? Why is the role of networks expanding?

– Explosion of OSNs(On-line Social Networks)– Data availability

• Rise of the Web 2.0 and Social media

– Universality • Networks from various domains of science, nature, and technology

are more similar than one would expect

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MySpace

Network Structure Characteristics of networks

– Node degree distribution– Clusters– Diameter, sparse/dense– Attribute distributions– …

How are such characteristics obtained?– Node generation– Edge generation

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Dynamics of Networks How do nodes interact? Behaviors of nodes

– Diffusion of information– Spread of virus– Vote– Reference– …

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Diffusion, cascading, Propagation, spreading,Contagion

Viral marketingWord-of-mouth

Strong ties and Weak ties

Side Step - Epidemiology Hippocrates

– Epidemic & Endemic

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John Snow: London Cholera, 1854

Kermack, W.O. and McKendrick, A.G. (1927). A contribution to the mathematical theory of epidemics I. Proc.Roy.Soc. A 115, 700-721.

Side Steps Growth of Hotmail

– Story of a quick(est) success and a failure of JaxtrSMS– Timing, fortune, …

In what contexts recommendations work and not?– 지름신은언제강림하는가?

Rise and fall of Cyworld– Why big guys fail?

Why large churches getting larger?

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Representation Text, table, …

– Adam follows Bob and Eve– Bob follows Eve and Genie– Charlie follows Bob– Dave follows Bob and Eve– Genie follows Charlie and Eve

Graphic

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A

B

G

E

D

C

Graphics Always Good?

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Matrix Matrix A where element Aij is relation between node i

and j

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0 1 0 0 1 0

0 0 0 0 1 1

0 1 0 0 0 0

0 1 0 0 1 0

0 0 0 0 0 0

0 0 1 0 0 1

A B C D F G

A

B

C

D

E

G

Good for Analysis

Directed/Undirected Networks Undirected networks

– Links have no direction– Co-authoring of papers

Directed networks– Directed links (arcs)– Following– Refer

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Connectivity Connected

– There are paths between any pairs of nodes

Disconnected

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Components

Giant component

Bridge edge

Articulation point

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Connectivity of Directed Networks Strongly connected

– There are (directed) paths from one node to another node

Weakly connected– Connected if edges are replaced by undirected edges

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Neighbors Nodes that are directly connected

– One hop away node

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A JIH

GF

E

D

C

B

N(A) = {B,C}

Node degree: # of edges

Directed Graphs Properties

DAG (Directed Acyclic Graph)– Directed graph without cycles– If there is a path from u to v, then there is no path from v to

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A JIH

GF

E

D

C

B

Node degree: In-degree, Out-degree

In(A): Set of nodes that can reach to node A

Out(A): Set of nodes that can be reached from node A

SCC (Strongly Connected Component)

A set S of nodes– Strongly connected– Largest set containing S with the strong connectivity property

Find SCC– An SCC containing node A = In(A) ∩ Out(A)

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A JIH

GF

E

D

C

B

Note: A node belongs to only one SCC

Theorem & Observation Given a directed graph, construct a graph G’ such that

– Nodes: SCCs– Arcs: If there is a path in G between two SCCs Si and Sj,

then (Si, Sj) Є G’(E)

G’ is DAG

Giant Component– Large Component

Observation: – There is only one giant component in any reasonably large

networks

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Example - Web Directed graph

– Nodes: Pages– Links: Hyperlinks

Bird’s view of Web– Strongly connected– Shape of DAG

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Bow-Tie Structure A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins,

J. Wiener. Graph structure in the Web. Computer Networks, 33, 2000.

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Next Lecture Graph theory & Random network

– Easley&Klenberg: Chapter 2– Newman:

• Chapter 6• Chapter 12, pp397~408

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