# 淺談社會網絡分析

Introduction to Social Network Analysis

# 文月 (Meng-Ying Tsai)

• 聽說有八盤之類的奇妙綽號
• 台大兔子系四年級
• 偶而會在台大開源社出沒
• ❤: 喝淺焙咖啡、唱日卡、嚐甜食

Vertex

Edge

Vertex Set V(G)

Edge Set E(G)

Graph G = (V, E)

V = {1, 2, 3, 4}

E = {{1, 2}, {1, 3}, {1, 4},

{2, 3}, {3, 4}}

1

2

3

4

{1,2}

{1,3}

{2,3}

{1,4}

{3,4}

1

2

3

4

{1,2}

{1,3}

{2,3}

{1,4}

{3,4}

1 2 3 4
1 0 1 1 1
2 1 0 1 0
3 1 1 0 1
4 1 0 1 0

Cohesion

Centrality

Cluster

* 接下來皆以無向圖作舉例！

Cohesion

• Density
• Distance
• Connectivity

Density

Density

Distance

Connectivity

# Basic Construct

Density

D =

|E|

|V| * (|V|-1)

2

1

# of edge

# of total possible edge

100%

50%

Density

Distance

Connectivity

# Basic Construct

Distance

Six Degrees of Separation

3.57 Degrees of Separation

Density

Distance

Connectivity

# Basic Construct

Distance

geodesic distance d(x,y): shortest path from x to y

x

y

Density

Distance

Connectivity

# Basic Construct

Distance

diameter: largest geodesic distance between any pair of nodes

x

y

Density

Distance

Connectivity

Connectivity

Density

Distance

Connectivity

# Basic Construct

Connectivity

Density

Distance

Connectivity

point connectivity: the min # of nodes that must be removed to disconnect 2 nodes

x

y

1

2

Connectivity

Density

Distance

Connectivity

• Degree
• Closeness
• Betweenness
• Eigenvector

Centrality

# Basic Construct

Centrality

Degree Centrality: 該 node 的連線越多，centrality 越高

# Basic Construct

Centrality

Closeness Centrality: geodesic distance 加總取倒數，distance越短centrality越高。

QAQ"

# Basic Construct

Centrality

Betweenness Centrality: 越常座落在別人的 geodesic path，centrality 越高。

# Basic Construct

Centrality

Eigenvector Centrality: 基本概念為 degree centrality，跟越重要的 node 連，算分越高。

I'm here

>

Pigeon

Degree
Closeness
Betweenness

Eigenvector

Degree
Closeness
Betweenness
Eigenvector

Degree
Closeness
Betweenness
Eigenvector

Degree
Closeness
Betweenness

Eigenvector

• Clique
• K-core

Cluster

# Basic Construct

Cluster

n-Clique: a maximal subgraph in which every pair of vertices is connected by a path of length n or less

n-Clique
K-core

n=1

n=2

• maximal subgraph：再加入任一頂點就無法維持其性質
• 點跟點之間的距離 ≤ n

# Basic Construct

Cluster

n-Clique: a maximal subgraph in which every pair of vertices is connected by a path of length n or less

• 條件嚴格，形成 clique 難
• 每個 clique 都被視為一樣重要

n-Clique
K-core

n=1

n=2

# Basic Construct

Cluster

K-core: a subgroup is defined as k-core when member have directed ties to at least K other vertices.

n-Clique
K-core

K = 3

K = 2

K = 1

n-Clique
K-core

K = 3

K = 2

K = 1

Dark Web

Dark/Covert network!

# Cases

Dark Network

Krebs V.(2001).Mapping Networks of Terrorist Cells. Connections, 24(3)

911 hijacking data

trusted prior contacts

• 鬆散
• 連同組的都要 2 steps way 才能接觸
• 避免其中有人被揪出來，整個網絡被連根拔起

# Cases

Dark Network

Krebs V.(2001).Mapping Networks of Terrorist Cells. Connections, 24(3)

911 hijakcing data

trusted prior contacts + ties

• 太鬆散無法做事QQ
• 讓溝通的順利的meeting!
• 沒有需要時，立即進入冬眠狀態

# Cases

Dark Network

Hughes C.E., Chalmers J., Bright D.A., McFadden M. (2017) Social network analysis of Australian poly-drug trafficking networks: How do drug traffickers manage multiple illicit drugs? Social Networks, 51C

Poly-drug network

manager  resource provider

worker    wholesale supplier

# Cases

Dark Network

Hughes C.E., Chalmers J., Bright D.A., McFadden M. (2017) Social network analysis of Australian poly-drug trafficking networks: How do drug traffickers manage multiple illicit drugs? Social Networks, 51C

Poly-drug network

manager  resource provider

worker    wholesale supplier

• 什麼毒品都賣，都可以賣
• 沒有鬆散、去中心的特質

# Cases

Dark Network

Hughes C.E., Chalmers J., Bright D.A., McFadden M. (2017) Social network analysis of Australian poly-drug trafficking networks: How do drug traffickers manage multiple illicit drugs? Social Networks, 51C

K1

K37

K10~20

betweenness,

degree centrality 高

# Cases

Interesting cases

Managing Creativity in Small Worlds

https://pdfs.semanticscholar.org/9176/2c87d3e73db324322bc03f1e7acb1892786a.pdf

Inventors in Silicon Valley’s Largest Collaborative Cluster

# Cases

Interesting cases

https://projects.iq.harvard.edu/chinesecbdb

Population Density of Biographical Persons

men who obtained the jinshi degree （Putian, 1050-1100）

China Biographical Database Project (CBDB)

# Cases

Interesting cases

Network of Thrones https://networkofthrones.wordpress.com/

Thanks for listening (ゝ∀･)⌒☆

#### 淺談社會網絡分析

By Meng-Ying Tsai

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