Understanding Dynamics in Time-Dependent Networks: Graph Analysis in the Adult Interactome or What’s Your Number? Qawi K. Telesford1, Jonathan H. Burdette2, Paul J. Laurienti2 1 School of Biomedical Engineering and Sciences, Virginia Tech-Wake Forest University, Winston-Salem, NC 2 Department of Radiology, Wake Forest School of Medicine, Winston-Salem, NC Supported by: NIAA (AA019893) http://lcbn.wakehealth.edu

Overview: In the analysis of networks, it is customary to analyze a single The Adult Interactome at a Glance realization of a network from aggregate data. However, in many Gender Gender (Top 1%) cases node dynamics are ignored, which can lead to misleading The Kings and of Degree Degree interpretations. Node dynamics can also be difficult to describe Network Statistics 1. 1439 without using multiple realizations of the network. Here we investigate 2. Mark Wood 1349 Female Nodes: 40,283 3. Sean Michaels 1339 27% different methods for identifying important nodes in a network. The 4. John Strong 1299 Male Edges: 302,469 Female 47% main thrust of this study is to understand how the ranking and 5. Mark Davis 1293 53% Clustering Coefficient: 0.385 6. Steve Holmes 1274 Male classification of a node can change according to how its connectivity 73% Path Length: 4.732 7. David Perry 1266 is calculated. 8. 1263 Degree: 15.017 Male 9. Mr. Marcus 1256 Communities: 75 10. Erik Everhard 1216 Degree Years Active Ron Jeremy Number 1. 483 The Data: Performer Attributes 600 15 5 The adult film industry represents a highly dynamic, ever-evolving 2. Sharon Kane 372 Male: 18,962 3. Roxanne Hall 363 500 4 4. Sandra Romain 351 400 10 community with rich interconnectivity that continues to spread and 3 Female: 21,321 5. Sindee Coxx 341 300 grow each year. Here we analyze the giant component of scenes 2 Years Active: 2.3 years 6. Tiffany Mynx 333 200 5 between adult performers in a network we dub the Adult 7. Sharon Mitchell 331 Ron Jeremy Number: 3.174 100 1 Interactome. All data was collected from the Internet Adult Film 8. Ariana Jollee 327 Female Belladonna 327 0 0 0 Database (http://www.iafd.com), containing 40,283 performers 10. Felecia/Jada Fire 323 All Male Female All Male Female All Male Female spanning the time period 1969-2011. Each node represents a All Top 1% All Top 1% All Top 1% performer while every edge means both performers appeared in the same scene together.

How do you rank a node that evolves over time? Degree Persistence (kp) Degree What makes one node more important than another? Is it simply the number of connections? The adult interactome started with two performers in 1969 and has rapidly swollen to thousands of performers by the 2000’s. We developed several degree metrics to determine node ranking. 4 5

3 1 8 6 3 3

3 4

2 2 2 3 2 2

1 1 1 2 3 4 3 5 5 5 2 2 1 2 1 Degree Dominance (k-index)

1 3 2 2 3 2 Time-point 1 Time-point 2 Time-point 3

How far and deep do you spread? Degree Persistence (k ): A measure of node connectivity accounting p for edges that appear at multiple time-points. While k shows the extent of performer reach, k shows how deeply involved a performer p is with his or her connections.

1. Tom Byron 6 7 2. Mark Davis 3. David Perry 4. Peter North 4 1 5. Mark Wood 11 14 6. Steve Holmes 7. Sean Michaels 3 5 8. John Strong Male 9. Erik Everhard 6 7 10. Mr. Marcus = 1 = 2 1. Nina Hartley = 3 2. Sharon Kane 3. Sandra Romain 4. Sharon Mitchell 5. Tiffany Mynx 6. Jada Fire = 푡푓 7. Ariana Jollee 8. Felecia 9. Kylie Ireland Dynamic k Dynamic k-index 푝 푡 Female p 푘 � 푘 10. Katja Kassin 푡=푡0 Yes, size does matter. Degree Dominance (k-index): A measure of node dominance. For every time-point in node is normalized to the maximum degree at that time-point. Shows persistent and dominant nodes regardless of network size. 8000 7000 6000

5000 4000 index = 푡푓 3000 − Performers 푡 2000 푘 1000 푘 � 푡max 푡=푡0 푘 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year All Male Female 2 2 Nothing more than a flash in the pan. Dynamic kp Dynamic k-index 1. Tom Byron 1. James Deen 1. Unknown Male 4822-C 1 2. Peter North What if you have a very short yet prolific career? 2. Mr. Pete 2. Unknown Male 4822-A 3. Ron Jeremy 2 4 3 4 To understand how lifespan in the network affects ranking, 3. Marco Banderas Unknown Male 4822-B 4. 4. Mark Wood 3. Bill Hadley 2 2 5. Hershel Savage dynamic versions of kp and k-index were developed by 5. John Strong George Marconi 6. Mark Davis averaging over the number of years a performer was 6. Erik Everhard 5 6 7 Hadley V. Baxendale 7. Marc Wallice 1 3 7. Mick Blue Kirt Harmon 8. Sean Michaels active. These metrics highlight performers that appear 8. Steve Holmes Michael Gebe 9. Original Male briefly, yet provide a profound contribution to the network. 9. Jenner Richard Coburn 10. David Perry Male Male 8 9 10 10. Sascha Tony Royale/Yank Levine

1. Sharon Mitchell ½ ½ 1. Bobbi Starr 1. Unknown Female 4822 2. Nina Hartley Dynamic = 푡푓 2. Trina Michaels 2. Angela Castle 3. Sharon Kane 2 3 4 0 3. Kristina Rose Erin Lee ¼ 4. Tina Russell 푡=푡 푡 ∑ 푘 4. Tory Lane Jan Harmon 5. Vanessa del Rio 푝 ¾ 1 푘 5. Lauren Phoenix Linda Chapman 6. Bionca 푦 6. Hillary Scott 5 6 7 Leticia Torrez 7. Debi Diamond ½ ½ 7. Alexis Texas Nancy Willson 8. Darby Lloyd Rains 푡푓 − 8. Kelly Wells 8. Barbara Grumet 9. Dynamic −index = 푡 ¼ ¾ Female 0 푘 9. Katja Kassin 9. Susie Mann 10. Serena ∑푡=푡 Female Female 푘푡 푚푚푚 10. Annette Schwarz 10. Chantal Virapin Normalization 푘 푦