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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