Social Network Analysis: Lecture 3-Network Characteristics - …

Social Network Analysis: Lecture 3-Network Characteristics

Donglei Du (ddu@unb.ca)

Faculty of Business Administration, University of New Brunswick, NB Canada Fredericton E3B 9Y2

Donglei Du (UNB)

Social Network Analysis

1 / 61

Table of contents

1 Network characteristics Degree Distribution Path distance Distribution Clustering coefficient distribution Giant component Community structure Assortative mixing: birds of similar feathers flock together

2 The Poisson Random network: a benchmark Erdo?s-R?enyi Random Network (Publ. Math. Debrecen 6, 290 (1959)

3 Network characteristics in real networks 4 Appendix A: Phase transition, giant component and small

components in ER network: bond percolation

Donglei Du (UNB)

Social Network Analysis

2 / 61

Network characteristics

Degree distribution Path distribution Clustering coefficient distribution Size of the giant component Community structure Assortative mixing (a.k.a., homophily or Heterophily in social network)

Donglei Du (UNB)

Social Network Analysis

4 / 61

Degree distribution for undirected graph

1

2 5

3 4

6

Degree distribution: A frequency count of the occurrence of each degree. First the degrees are listed below:

node 1 2 3 4 5 6

degree 2 3 2 3 3 1

Donglei Du (UNB)

Social Network Analysis

5 / 61

Degree distribution for undirected graph

The degree distribution therefore is:

degree 1 2 3

frequency 1/6 2/6 3/6

Average degree: let N = |V | be the number of nodes, and L = |E| be the number of edges:

n

deg(i)

K = i=1

2L =

N

N

k = 2(7)/6 = 7/3 for the above graph.

Donglei Du (UNB)

Social Network Analysis

6 / 61

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download