Link Analysis

1
Link Analysis

• 2001. 1. 31
• Sekyoung Youm

2
Contents

• Introduction
• Graph theory
• Some basic graph theory
• Seven Bridges of Konigsberg
• Traveling salesman problem
• Case study
• Conclusion

3
Introduction

• Link Analysis
• Analyzing telephone call patterns
• Understanding physician referral patterns
• Combining leads

4
Graph theory

• What is a graph?
• is an abstraction developed specifically to
  represent relationships

• Node(vertex)
• Edge
• Fully-connected
• Planar
• Degree
• Loop
• Path
• Cycle
• Component

D14 E 7
5
Graph theory

• A breeder, a ram, a wolf, cabbage. problem

A breeder
A breeder
( bre, wolf, ram, cab / 0 ) a ( bre, wolf, ram /
cab ) b ( bre, wolf, cab / ram ) c ( bre,
ram, cab / wolf ) d ( bre, ram / wolf, cab )
e
a ( wolf, cab / bre, ram ) b ( wolf / bre, ram,
cab ) c ( ram / bre, wolf, cab ) d ( cab / bre,
wolf, ram ) e ( 0 / bre, wolf, ram, cab)
a?a?c?d?d?c?e?e
6
Graph theory

• Directed graphs
• Source node
• Sink node
• Cycle
• Detecting cycles in a graph
• Remove the source and sink node

7
Seven Bridges of Konigsberg

• Is it possible to walk over all seven bridges
  exactly once?
• The pregel river in Konigsberg has two islands
  connected by a total of seven bridges

8
Eulerian Path

• Eulerian path
• exist only when the degrees of all the nodes in
  a graph are even, except at most two
• Path 1,5,6,7,8,9,10,12,13,14,15,11,2,3,4
• Seven Bridges of Konigsberg
• There are four nodes
• whose degrees are odd

9
Traveling Salesman problem

• Hamiltonian path
• a path that visits all nodes in a graph exactly
  once
• Weight graph
• the shortest path ABCDE(24)
• Greedy algorithm
• CDBEA(32)

(yes)
(no)
(no)
10
Graph Coloring Algorithm

• Complete graph the number of node
• Cyclic graph whose of node and edge are equal
• of node is odd3
• of node is even2

A
C
D
B
11
Case study

• Who is using fax machines from home?
• The data
• Several types of fax machine usage
• Dedicated fax(only for fax communication)
• Shared(voice calls)
• Data(via fax or via computer modem)

12
Approach

• The process used to find fax machines
• graph coloring algorithm
• a call graph for 15 numbers and 19 calls

• Fax
• Shared
• Voice
• Unkown

13
Approach(cont)

• Short calls removed and nodes is labeled as
  fax, unknown, and information
• Nodes connected to the initial fax machines are
  assigned the fax label
• Those connected to information are assigned the
  voice label
• Those connected to both, are shared.
• The rest are unknown

14
Conclusion

• Strengths of link analysis
• Most Appropriate for Linked Data
• Useful for Visualization
• Creates Derived Attributes
• Weakness of link Analysis
• Not Applicable to Many Types of Data
• Few Tool
• Inefficient in SQL