Post on 30-Jun-2015
description
EXPLORAT
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NETWORK AS A MEDIA
• Transmission Flow• Information• Goods• Service
• Network Analysis is to STUDY• Critical Actors Vertex Centrality• Critical Path• Diffusion Rate Network Centralization
VERTEX CENTRALITY
HM-1: Articular the Diffusion through all Regions
HP -6: In Case of Malfunction Not a Disaster
NETWORK CENTRALIZATION
Looks CounterintuitiveThe More Number of Central Vertex Cause Less Compact Network
The More VARIATION in Vertices Centrality Higher Network Centralization
Vertex Centrality DEFINES Network Centralization
1 Most, 4 Least Central 3 Most, 2 Least Central
DEFINITION: TWO PERSPECTIVE
Vertex Reachability Vertex Intermediary
How Easily the Information Reach a Vertex How Easily a Vertex can Disseminate the Information
How much Information Traffic is Relayed
DEGREE CENTRALITY: UNDIRECTED NET
• Degree Centrality of a Vertex Vertex Degree
• Degree Centralization of a Network
𝑀𝑎𝑥𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛𝑉𝑎𝑙𝑢𝑒=3∗ (3−1 )+1∗ (3−3 )=6 𝑀𝑎𝑥𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛𝑉𝑎𝑙𝑢𝑒=12 𝑀𝑎𝑥𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛𝑉𝑎𝑙𝑢𝑒=20
For Directed Network this Definition will not Work!
SAMPLE
𝐷𝑒𝑔𝑟𝑒𝑒𝐶𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑧𝑡𝑖𝑜𝑛=0
𝐷𝑒𝑔𝑟𝑒𝑒𝐶𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑧𝑡𝑖𝑜𝑛=1 𝐷𝑒𝑔𝑟𝑒𝑒𝐶𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑧𝑡𝑖𝑜𝑛=0.17
CLOSENESS CENTRALITY
• Degree Centrality has Local View of Vertex Neighborhood
• Global View• Distance to all Other Vertices: The Closer Path The Faster
Diffusion
• Geodesic Shortest Path Between Two Vertices
• Distance Length of Geodesic Path
• Closeness Centrality of a Vertex
• Closeness Centralization of a Network
𝑀𝑎𝑥𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛𝑉𝑎𝑙𝑢𝑒= (𝑛−1 )× [1+2× (𝑛−2 )−1 ]=24𝑀𝑎𝑥𝐶𝑣=1 𝑖𝑛𝑆𝑡𝑎𝑟 −𝑁𝑒𝑡𝑤𝑜𝑟𝑘
BETWEENNESS CENTRALITY
• Intermarry Vertex, Relaying NodeHow Many Flows of Information are Disrupted or Must Make Longer Detours if a Vertex Stops Passing on Information!
Betweenness Centrality of a Vertex The Proportion of all Geodesics Between Pairs of Other Vertices that Include This Vertex
Betweenness Centralization
Degree Centralization =
Closeness Centralization =
PAJEK
Network > Create Partition > Degree
Network > Create Partition > k-Neighbors
Network > Create New Network > SubNetwork with Paths > All Shortest Path between Two Vertices
PAJEK
DegreeCloseness
Betweenness