CDT Matthew R Webb
1 November 2006
ARL/USMA Technical Symposium

• What is Dynamic Social Network Analysis?
– Network Measures
– Statistical Process Control
• Application: Al-Qaeda
– Method
– Preliminary Results
• Future Research
• Questions

What is Dynamic Network
Analysis?
• Social Network Analysis (SNA) is the mathematical methodology of quantifying connections between individuals and groups.
• Dynamic SNA compares snapshots of a network over time to determine when the network changes.
Time
Experience

• Key Network Measures
– Density
– Degree Centrality
– Closeness Centrality
– Betweeness Centrality
– Diameter
Graph courtesy of Steve Borgatti

• Calculates a statistic from sequential measurements of a random process and compares it to a control limit.
• Used extensively in quality engineering.
– Example cutting boards at a lumber mill

• Cumulative-Sum Control Chart
– Good at detecting small changes in mean over time
– Built in change point detection
• Calculate Z i
Z value for each time-period.
i

 x i
 
0

/

• Two Charts (To Detect Increase and Decrease)
C t
  max{ 0 , Z t
 k

C t


1
}
C t
  max{ 0 ,

Z t
 k

C t


1
}

• The Office of Naval Research maintains network data on Al-Qaeda.
• Ran CUSUM Control Chart for three Network
Measures (Betweeness, Closeness, and Density)
0.012
0.01
0.008
0.006
0.004
Betweeness
Density
Closeness
0.002
0
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Time

The control chart signals a change in the network in
2000/2001.
Closeness
Z
C+
C-
1994
0.0027
-0.8729
0
0.3729
1995
0.003
1996
0.0028
1997
0.0028
1.0911
-0.2182
-0.2182
0.5911
0 0
0 0 0
1998
0.0031
1.7457
1.2457
0
1999
0.003
1.0911
1.8368
0
2000
0.0032
2.4004
3.7372
0
2001
0.0034
2002
0.0024
2003
0.0015
2004
0.0004
3.7097
-2.8368
-8.7287
-15.9299
6.9469
3.6101
0 0
0 2.3368
10.5655
25.9955
Signal 0 0 0 0 0 0 0 1
A MLE of the change point is
1997.
- Increased activity of IG
Bright Star ’97 cut short
Feb ’98 Islamic Front
Embassy bombings in ’98
1997 was THE critical planning year for Al-Qaeda.
4
3
2
1
0
8
7
6
5
Closeness CUSUM Chart for Al-Qaeda (1994-2004)
Signal
Change Point
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

• New Data
– IkeNet and TOEP Data
• Near-Complete Network Picture
• More Snapshots
• New Approaches
– What if Network Picture is Incomplete?
– What Network Measures are the most telling?
– Which Control Chart work best?