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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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