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Dynamic Competition Networks: Detecting Alliances and Leaders

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Algorithms and Models for the Web Graph (WAW 2018)

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Abstract

We consider social networks of competing agents that evolve dynamically over time. Such dynamic competition networks are directed, where a directed edge from nodes u to v corresponds a negative social interaction. We present a novel hypothesis that serves as a predictive tool to uncover alliances and leaders within dynamic competition networks. Our focus is in the present study is to validate it on competitive networks arising from social game shows such as Survivor and Big Brother.

Research supported by grants from NSERC, Ryerson University, NSF CCF-1149756, IIS-1546488, NSF Center for Science of Information, CCF-0939370, DARPA SIMPLEX.

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A Appendix

A Appendix

Complete data from all U.S. Seasons of Survivor and Big Brother may be found in the document:

http://www.math.ryerson.ca/~abonato/papers/SurvivorBB_Data_BEGM.

We include this data below for convenience. The data from five of these seasons (Survivor: Borneo, China, Game Changers, HHH, and Big Brother 12) is discussed in detail in the body of the paper. We provide the remaining data to further support the DCH and for transparency.

All data was gathered from the Survivor and Big Brother Wiki pages [2, 18]. Within the wiki, each season has a dedicated page (for example http://survivor.wikia.com/wiki/Survivor:_Millennials_vs._Gen_X) with a table of voting history, which was used to construct the directed networks. Each player of the game is a vertex of the network, with a directed edge added from vertex A to vertex B if player A voted against player B. If player A voted against player B n times, then the edge has a weight of n. We scraped voting history tables using simple python code, and further did the analysis in python.

Appendix A.1 gives a table for each season with the following metrics, which are discussed thoroughly in Sect. 2:

  1. 1.

    In-degree;

  2. 2.

    Out-degree;

  3. 3.

    Closeness;

  4. 4.

    CON Score.

Contestants are listed in the order which they were voted out, where the player on top of the table remained in the game the longest.

Appendix A.2 gives the edge density for every Alliance in each season, as well as the edge density of the full graph for comparison. Information on edge density can be found in Sect. 2.

1.1 A.1 Complete Network Metrics

figure f
figure g
figure h
figure i
figure j
figure k
figure l
figure m

1.2 A.2 Complete Alliances Data

Season

Winner

Finalists

Alliances

ED

Full ED

Africa

Ethan

Kim J.

Older Samburu: Frank, Teresa, Linda, Carl

0.167

0.85

Boran: Lex, Ethan, Kim J., Tom, Kelly

1.0

Younger Samburu: Silas, Kim P., Brandon, Lindsey

0.167

All-Stars

Amber

Rob M.

Chapera: Rob M., Amber, Jenna L., Rupert, Tom, Alicia

1.067

0.581

Mogo Mogo: Lex, Shii Ann, Kathy, Jerri

0.667

Blood vs. Water

Tyson

Monica, Gervase

Singles: Tyson, Monica, Gervase, Ciera, Hayden, Caleb

1.667

0.747

Five Guys: Hayden, Brad, John, Caleb, Vytas

0.9

Galang: Tina, Aras, Tyson, Monica, Gervase

1.3

Borneo

Richard

Kelly

Barbecue: Colleen, Jenna, Gervase

1.667

0.783

Tagi: Richard, Rudy, Susan, Kelly

1.5

Cagayan

Tony

Woo

Solana: Trish, Jefra, LJ, Tony, Woo

0.7

0.647

Aparri: Spencer, Tasha, Jeremiah, Morgan, Sarah, Kass

0.533

Cambodia

Jeremy

Spencer, Tasha

Bayon: Jeremy, Tasha, Stephen, Andrew, Keith, Joe, Kimmi

0.905

0.705

Witches’ Coven: Kelley, Abi-Maria, Ciera, Kass

0.167

Caramoan

Cochran

Dawn, Sherri

Stealth R Us: Cochran, Dawn, Phillip, Andrea, Malcolm, Corinne

0.8

0.742

Gota: Sherri, Julia, Shamar, Laura, Michael, Matt

0.667

Cool Kids: Eddie, Reynold, Hope, Allie

0.0

China

Todd

Courtney, Amanda

Fei Long: Todd, Courtney, Amanda, Aaron, Denise, James, Frosti

0.667

0.75

Zhan Hu: Peih-Gee, Erik, Jaime

0.0

Cook Islands

Yul

Ozzy, Becky

Aitu Four: Yul, Ozzy, Becky, Sundra

1.0

0.611

Raro: Adam, Parvati, Candice, Nate, Jonathan

0.9

Fiji

Earl

Cassandra, Dreamz

Four Horsemen: Alex, Mookie, Edgardo, Dreamz

0.667

0.66

Syndicate: Earl, Cassandra, Michelle, Yau-Man

0.667

Season

Winner

Finalists

Alliances

ED

Full ED

Gabon

Bob

Susie, Sugar

Onion: Bob, Corinne, Randy, Charlie, Marcus, Jacquie, Susie

0.476

0.667

Fang: Ken, Crystal, Kelly, G.C., Susie, Sugar, Matty

1.095

Game Changers

Sarah

Brad, Troyzan

Power Six: Sarah, Brad, Troyzan, Sierra, Debbie, Tai

0.933

0.737

Tavua: Aubry, Cirie, Michaela, Ozzy, Andrea, Zeke, Sarah

1.238

Guatemala

Danni

Stephenie

Nakum: Stephenie, Rafe, Lydia, Cindy, Judd, Jamie

1.067

0.712

Yaxha: Danni, Bobby Jon, Brandon, Blake

0.333

Heroes vs. Healers vs. Hustlers

Ben

Chrissy, Ryan

Healers: Joe, Desi, Jessica, Cole, Mike

0.6

0.706

The Round Table: Chrissy, Ryan, Devon, JP, Ben, Ashley, Lauren

0.905

Final Four: Ashley, Lauren, Ben, Devon

1.333

Heroes vs. Villains

Sandra

Parvati, Russell

Heroes: Rupert, Amanda, J.T., Cirie, James, Candice

0.533

0.679

Rob’s Villains: Sandra, Courtney, Rob, Tyson, Jerri, Coach

0.667

Russell’s Villains: Parvati, Russell, Jerri, Danielle

1.0

KR

Michele

Aubry, Tai

Gondol: Jason, Julia, Scot, Tai

1.0

0.625

Dara Women: Michele, Aubry, Joe, Cydney, Julia, Debbie

0.8

Marquesas

Vecepia

Neleh

Maraamu: Rob, Vecepia, Sean, Rob, Sarah

0.3

0.733

Rotu Four: John, Robert, Tammy, Zoe

0.667

Outsiders: Kathy, Vecepia, Neleh, Paschal, Sean

1.0

Micronesia

Parvati

Amanda

Black Widow Brigade: Parvati, Amanda, Cirie, Natalie, Alexis

1.0

0.563

Malakal Couples: James, Ozzy, Parvati, Amanda, Cirie

0.5

Older Airai: Tracy, Kathy, Chet

0.0

Millennials vs. Gen X

Adam

Hannah, Ken

Triforce: Jay, Will, Taylor, Michelle, Figgy, Michaela

0.267

0.768

David’s Vinaka: Hannah, Ken, Jessica, David, Adam

0.6

Zeke’s Vinaka: Bret, Jay, Sunday, Zeke, Will

0.7

Takali: Bret, Sunday, Chris, Lucy, Paul, Jessica

0.733

Nicaragua

Fabio

Chase, Sash

Final Four: Chase, Sash, NaOnka, Holly, Jane

0.7

0.674

La Flor: Kelly S., Brenda, Chase, Sash, NaOnka

0.4

Espada: Dan, Marty, Jill

0.0

One World

Kim

Sabrina, Chelsea

Misfit: Leif, Jonas, Colton, Tarzan, Troyzan

0.3

0.765

Muscle: Michael, Matt, Jay, Bill

1.0

Salani: Kim, Sabrina, Chelsea, Alicia, Kat

0.9

Palau

Tom

Katie

Koror: Tom, Katie, Ian, Jenn, Gregg

1.0

0.588

Season

Winner

Finalists

Alliances

ED

Full ED

Panama

Aras

Danielle

La Mina: Terry, Austin, Nick, Dan

0.667

0.65

Casaya: Shane, Courtney, Bruce, Aras, Danielle, Cirie

1.067

Pearl Islands

Sandra

Lillian

Morgan: Andrew, Ryan O., Osten, Darrah, Tijuana

0.2

0.8

Drake: Rupert, Sandra, Christa, Jon, Trish

0.8

Outcast: Burton, Jon, Tijuana, Lillian, Darrah

1.9

Philippines

Denise

Lisa, Michael

Matsing: Denise, Malcolm, Angie

1.333

0.654

Kalabaw: Carter, Jonathan, Jeff

0.0

Fulcrum: Michael, Lisa, R.C

0.0

Tandang: Abi-Maria, Pete, Artis, R.C., Lisa, Michael

0.533

Redemption Island

Rob

Philip, Natalie

Zapatera Six: Mike, Ralph, Steve, Julie, David, Sarita

0.467

0.895

Stealth R Us: Rob, Phillip, Natalie, Ashley, Andrea, Matthew, Grant

1.571

Russell’s Zapatera: Stephanie, Krista, Russell

0.0

Samoa

Natalie

Russell H., Mick

Galu: Brett, Monica, Dave, Laura, Kelly, Shambo, John

0.667

0.663

Foa Foa Four: Natalie, Russell H., Mick, Jaison

0.667

San Juan del Sur

Natalie

Jaclyn, Missy

Fab Five: Missy, Baylor, Jaclyn, Jon, Natalie

1.2

0.752

Coyopa Guys: Alec, Wes, Josh, Dale, John

0.3

South Pacific

Sophie

Coach, Albert

The Family: Sophie, Coach, Albert, Rick, Brandon, Edna

1.2

0.922

Savaii: Ozzy, Whitney, Dawn, Keith, Jim, Elyse, Cochran

1.143

Thailand

Brian

Clay

Sook Jai: Jake, Penny, Ken, Erin, Shii Ann

1.0

0.683

Chuay Gahn Five: Brian, Clay, Jan, Helen, Ted

1.2

The Amazon

Jenna

Matthew

Tambaqui: Roger, Matthew, Rob, Butch, Dave, Alex

1.133

0.767

Jaburu: Jenna, Heidi, Alex, Deena, Shawna, Rob, Matthew

1.048

The Australian Outback

Tina

Colby

Ogakor: Amber, Jerri, Tina, Colby, Keith

1.0

0.825

Kucha: Elisabeth, Rodger, Nick, Alicia, Jeff

0.0

Tocantins

J.T.

Stephen

Exile: Sierra, Brendan, Stephen, Taj

0.667

0.675

Timbira: Coach, Tyson, Debbie

0.333

Jalapao Three: J.T., Stephen, Taj

0.667

Vanuatu

Chris

Twila

Yasur: Ami, Leann, Lisa, Twila, Scout, Eliza

1.2

0.719

Final Four: Chris, Twila, Scout, Eliza

1.333

Fat Five: Chris, Chad, Lea, Rory, Travis

0.3

Worlds Apart

Mike

Carolyn, Will

Escameca: Rodney, Dan, Kelly, Mike, Sierra

1.0

0.739

Nagarote: Jenn, Joe, Hali, Will

1.0

Season

Winner

Finalists

Alliances

ED

Full ED

10

Dan

Memphis

The Renegades: Dan, Memphis

0.0

0.718

The Coven: Keesha, Libra, April

0.667

12

Hayden

Lane

The Brigade: Enzo, Hayden, Lane, Matt

0.5

0.718

13

Rachel

Porsche

The Regulators: Dominic, Keith, Cassi, Lawon

0.5

0.821

Newbies: Adam, Porsche, Kalia, Shelly, Lawon, Dominic, Cassi, Keith

0.786

Veterans: Daniele, Dick, Jordan, Rachel, Jeff, Brendon

0.467

14

Ian

Dan

Silent Six: Britney, Danielle, Dan, Frank, Mike, Shane

0.8

0.581

Team Toche: Britney, Shane, Danielle, Dan

0.667

The Quack Pack: Britney, Danielle, Dan, Ian, Shane

0.6

Chilltown 2.0: Mike, Frank

0.0

15

Andy

GinaMarie

Tenexas: Judd, Jessie

1.0

0.767

Exterminators: GinaMarie, Andy, Judd, Spencer

0.667

Young Grasshoppers: GinaMarie, Howard, Andy, Kaitlin, Spencer, Judd

0.733

The Moving Company: Nick, McCrae, Spencer, Jeremy, Howard

0.6

3 A.M.: Aaryn, Amanda, Andy, McCrae

0.5

The Blonde-Tourage: David, Aaryn, Kaitlin, Jeremy, GinaMarie, Jessie

0.4

The Goof Troupe: Amanda, Andy, McCrae, Judd

1.167

The Mom Squad: Elissa, Helen

0.0

Season

Winner

Finalists

Alliances

ED

Full ED

16

Derrick

Cody

The Detonators: Christine, Cody, Derrick, Frankie, Zach

0.6

0.808

The Crazy 8’s: Amber, Cody, Devin, Donny, Frankie, Joey, Nicole, Paola

0.929

El Cuatro: Amber, Joey, Nicole, Paola

0.833

Team America: Derrick, Donny, Frankie, Joey

1.0

The Bomb Squad: Amber, Caleb, Christine, Cody, Derrick, Devin, Frankie, Hayden, Zach

0.722

Los Tres Amigos: Cody, Derrick, Zach

0.333

The Hitmen: Cody, Derrick

0.0

Zankie: Frankie, Zach

0.0

The Rationale: Cody, Derrick, Hayden, Nicole

1.0

The Double D’s: Donny, Devin

1.0

The Weirdos: Christine, Hayden, Nicole

0.667

17

Steve

Liz

Clelli: Clay, Shelli

0.0

0.765

ShellTown: Jace, Austin

1.0

Team JJ: Jackie, Jeff

0.0

Students of Sound: Steve, Vanessa

1.0

Three’s Company: Clay, Shelli, Vanessa

0.333

The Goblins: James, Jackie, Meg, Audrey, DaVonne, Jason, Jeff

0.667

The Sixth Sense: Clay, Austin, Julia, Liz, Shelli, Vanessa

0.667

Jecky: Becky, John

0.0

Austwins: Austin, Julia, Liz, Jace

0.5

Scamper Squad: Vanessa, Liz, Steve, Austin, Julia

0.5

Rockstars: John, Steve

0.0

18

Nicole

Paul

The Revolution: Paul, Jozea, Victor

0.0

0.819

Team PP: Paulie, Paul

2.0

Nicorey: Corey, Nicole

0.0

Zaulie: Paulie, Zakiyah

0.0

Spy Girls: Natalie, Bronte, Bridgette

0.0

Fatal Five: DaVonne, Michelle, Nicole, Tiffany, Zakiyah

0.6

Final Four: Corey, Nicole, Paul, Victor

0.833

8-Pack: Nicole, James, DaVonne, Frank, Tiffany, Corey, Michelle, Zakiyah

0.75

Jatalie: James, Natalie

0.0

The Executives: Corey, James, Paul, Paulie, Victor

1.2

The Sitting Ducks: Paul, Victor

0.0

19

Josh

Pau

The Team: Christmas, Cody, Dominique, Elena, Jessica, Mark, Matt, Paul, Raven

1.028

0.824

Marlena: Elena, Mark

0.0

Jody: Cody, Jessica

0.0

The Misfits: Christmas, Josh, Paul

1.0

Whistlenut and Ole: Alex, Jason, Paul

1.0

2

Will

Nicole

Chilltown: Mike, Will, Shannon

0.333

0.691

TOP (The Other People): Bunky, Kent, Nicole, Hardy, Monica, Autumn

0.733

Season

Winner

Finalists

Alliances

ED

Full ED

3

Lisa

Danielle

Danielle and Jason: Danielle, Jason

0.0

0.803

Chiara and Roddy: Chiara, Roddy

0.0

Cartel: Lisa, Chiara, Tonya, Roddy, Eric, Josh

0.667

Original Six: Josh, Roddy, Lisa, Chiara, Eric, Gerry

0.933

Eric and Lisa: Eric, Lisa

0.0

4

Jun

Alison

Three Stooges: Jee, Justin, Robert

0.333

0.697

Girl Power: Alison, Erika, Jun

0.333

Elite Eight: Alison, Dana, David, Erika, Jack, Jun, Nathan, Scott

0.464

5

Drew

Michael

Four Horsemen: Drew, Jase, Michael, Scott

0.167

0.692

Pinky Swear: Adria, Diane, Karen, Natalie, Nakomis, Will

0.667

6

Ivette

Maggie

Sovereign Six: Janelle, Howie, Kaysar, James

1.333

0.813

The Friendship: Ivette, Maggie, Eric, Beau, Jennifer, April

0.667

8

Dick

Daniele

Mrs. Robinson: Zach, Kail, Nick, Mike

0.5

0.736

Late Night Crew: Amber, Daniele, Dick, Dustin, Eric, Jameka, Jessica

0.619

9

Adam

Ryan

Team Christ: Adam, Ryan, Sheila, Natalie

1.333

0.724

All-Stars

Mike

Erika

Sovereign Six: Janelle, Howie, Kaysar, James

0.5

0.725

Chilltown: Mike, Will

0.0

Mr. and Mrs. Smith: Diane, Jase

1.0

The Legion of Doom: Danielle, James, Mike, Will

0.5

Over The Top

Morgan

Jason, Kryssie

OTT Jamboree: Jason, Justin, Kryssie, Scott, Shelby

0.6

0.603

Boys Alliance: Cornbread, Monte, Scott, Shane

0.667

The Ballsmashers: Alex, Morgan, Shelby, Whitney

0.0

Late Night Jamboree: Danielle, Jason, Justin, Kryssie, Shane

0.6

The Southerners: Alex, Monte, Morgan, Shane, Whitney

0.4

The Jackolanterns: Jason, Kryssie, Neeley

0.333

Shonte: Monte, Shane

1.0

Shanielle: Danielle, Shane

0.0

Monte and His Pythons: Alex, Monte, Morgan, Shelby, Whitney

0.0

Krason: Jason, Kryssie

1.0

Sisters: Alex, Morgan

0.0

Team Longshot: Morgan, Shelby

0.0

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Bonato, A., Eikmeier, N., Gleich, D.F., Malik, R. (2018). Dynamic Competition Networks: Detecting Alliances and Leaders. In: Bonato, A., Prałat, P., Raigorodskii, A. (eds) Algorithms and Models for the Web Graph. WAW 2018. Lecture Notes in Computer Science(), vol 10836. Springer, Cham. https://doi.org/10.1007/978-3-319-92871-5_9

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