Social Media Mining: An Introduction

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CUUS2079-06 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:15

164 Community Analysis

(a) Physics Citations

103

104

105

102

102 103 104 105

106

(b) Patent Citations

Number of edges

Number of nodes

106

107

105

105 106 107

108

Number of edges

Number of nodes

Jan 1993 Edges 1975

1999

Apr 2003

= 0.0113 x1.69 R^2 =1.0 Edges= 0.0002 x1.66 R^2 =0.99

Figure 6.12. Graph Densification (from [Leskovec et al., 2005]).

Diameter Shrinkage

Another property observed in large networks is that the network diameter

shrinks in time. This property has been observed in random graphs as well

(see Chapter 4). Figure6.13depicts the diameter shrinkage for the same

patent network discussed in Figure6.12.

In this section we discussed three phenomena that are observed in evolv-

ing networks. Communities in evolving networks also evolve. They appear,

35

30

25

20

Effective diameter^15

10

5

1975 1980 1985 1990

Time [years]

1995 2000

Figure 6.13. Diameter Shrinkage over Time for a Patent Citation Network (from

[Leskovec et al., 2005]).