Two-Mode Tie Formation in Creative Collaborative Networks

Benjamin Lind, Stanislav Moiseev, and Georgy Mkrtchyan

National Research University - Higher School of Economics

Creative Collaboration

  • Considerable previous literature on formal collaborations
    • Bureaucratic organizations
    • E.g., work groups, academic papers, films
  • Relatively less research on creative collaboration networks (though see Uzzi and Spiro 2005)
    • Should resemble a mixture of formal collaborations and voluntary groups
    • Likely formed following some of the general mechanisms leading to formal collaborations

Collaboration is a Two-Mode Process

  • Actors (mode one) and projects (mode two)
    • Projects represent an organization
    • As an organization, projects can act
  • Ambiguous agency (Brieger 1974)
    • Sometimes actors create and join projects
    • Sometimes projects recruit actors
  • We cannot assume that tie formation is driven exclusively by the actors

Collaboration is a Dynamic Process

  • All networks are dynamic networks (Barabási)
  • A project begins and ends at particular times
  • Actors join and acquire experience through participating in a series of projects

Our Interest

How do ties form in the context of creative collaborative networks?

Popular Explanations for Tie Formation

(Crossley [2009]; McPherson, Smith-Lovin, and Cook [2001]; Powell, White, Koput, and Owen‐Smith [2005]; Rivera, Soderstrom, and Uzzi [2010])

Preferential Attachment

  • Right-skewed degree distribution (Barabási and Albert 1999)
    • Older actors in the network
    • New actors latch onto the ones already popular
  • Implications for two-mode collaborative projects
    • The cumulative number of projects an actor collaborates on should increase at an increasing rate over time
    • The cumulative number of collaborators a project has should grow at an increasing rate

Homophily

  • Similar actors tend to collaborate
  • Similar projects tend to share the same actors
  • Characteristics of similarity
    • Common age (actor) and period (project)
    • Gender (actor)
    • Shared geography (actor and project)
    • Creative aesthetics (actor)
    • Institutional affiliation (project)

First Order Closure

(Robins and Alexander 2004)

  • Actors who have previously collaborated on a project likely continue the relationship
    • Basis for group identity on collaborative projects
    • Builds trust and reliability in project

First Order Closure

(Robins and Alexander 2004)

Lesser Discussed Explanation

Second Order Closure

(Opsahl 2013)

  • Do I work with someone my collaborator has experience with, but I do not?
    • Yes
      • Short path length means quicker search (Granovetter 1974 weak ties)
      • Commonalities likely (i.e., cohesive subgroups)
    • No
      • My collaborator knows her, so I know of her, and if I wanted to work with her I would already be doing so with both her and my collaborator (Granovetter 1974 strong ties)
      • Shifts power balance (Bearman, Moody, and Stovel 2004)

Second Order Closure

?

Limitations of Projecting Two-Mode to One-Mode Networks

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Data

Encyclopaedia Metallum: The Metal Archives

Metal Archives: Search Results

Metal Archives: Band Page

Metal Archives: Band Members

Metal Archives: Musician Page

Metal Archives: Album Page

Network Descriptives

  • Size
    • Musicians, Recordings: 499,600, 258,922
    • Edges: 805,923 (density = 6.23e-06)
    • Largest component
      • Musicians, Recordings: 225,980, 132,568
      • Edges: 689,575
    • Mean Degree
      • Musician, Recording: 1.88, 3.64
  • Age (min, 25%ile, med, 75%ile, max)
    • Musician birth: 1898, 1974, 1982, 1988, 2009
    • Album release: 1968, 2000, 2006, 2010, 2015
  • Record labels: 22,942
  • Nationalities: 160
  • Females: 6%

To keep it manageable, we'll focus on three record labels

  • Earache Records
    • Founded 1985, UK
    • Grindcore, death metal, thrash, and industrial metal
    • 323 releases (12th) and 892 musicians
  • Candlelight Records
    • Founded 1993, UK
    • Black and death metal
    • 288 releases (14th) and 1288 musicians
  • Season of Mist
    • Founded 1996, France
    • Black, pagan, death, avant-garde, and gothic metal
    • 260 releases (16th) and 1313 musicians

Findings

Preferential Attachment

Power Law Fit (Kolmogorov-Smirnov test)

  • Musicians (degree >= 10): Earache Records, Season of Mist
  • Recordings (degree >= 12): All

Measurement and Tests

  • Local effects
    • Homophily: neighborhood of order 1
    • Closure: neighborhood of order 2, 4
  • Measurements
    • Homophily
      • Blau index of diversity (categorical)
      • Standard deviation (continuous)
    • Closure
      • Robins and Alexander, 2004
      • Opsahl 2013
  • Test: Wilcoxon Signed-Rank (paired)
    • Compare observed distributions to those from 1000 rewired graphs

Homophily, Country

Wilcoxon Signed-Rank Tests with p-values < 0.05

  • Earache: 100%
  • Candlelight: 100%
  • Season of Mist: 100%

Homophily, Age

Wilcoxon Signed-Rank Tests with p-values < 0.05

  • Earache: 100%
  • Candlelight: 100%
  • Season of Mist: 99%

Homophily, Gender

Wilcoxon Signed-Rank Tests with p-values < 0.05

  • Earache: 20%
  • Candlelight: 75%
  • Season of Mist: 85%

First Order Closure

Wilcoxon Signed-Rank Tests with p-values < 0.05

  • Earache: 100%
  • Candlelight: 100%
  • Season of Mist: 100%

Second Order Closure

Wilcoxon Signed-Rank Tests with p-values < 0.05
(two-tailed)

  • Earache: 14%
  • Candlelight: 57%
  • Season of Mist: 99%
    • (Greater among the observed)
    • Does not hold in p*

Summary of Findings

  • Preferential Attachment
    • Power law effects on the right tail
  • Homophily
    • Very strong nationality and age effects
    • No gender effects
  • Closure
    • First Order: very strong effects
    • Second Order
      • Not substantively different from chance for two of the three subgraphs
      • Greater among one subgraph, though not robust
  • Consistency across subgraphs after controlling for size

Conclusions

  • Collaboration forms ties between people and projects
    • People do not necessarily form a direct tie to one another
      • Neither do projects
    • Both people and their projects have some degree of agency
  • Traditional tie formation explanations do hold when analyzed as a two-mode process
  • Closure takes on a different character in two-mode networks
    • No definitive indication of weak ties in collaboration
    • Lengthy, careful search for collaborators is likely

Remaining Questions

  • Do these findings hold for other types of music?
    • I.e., jazz, hip hop
  • Do these findings exist in other forms of collaboration?
    • I.e., co-authorship
  • Do these findings remain in multivariate analyses?

How common are closed five-paths?

Thank You!

Questions, comments, or advice?

Benjamin Lind (lind.benjamin@gmail.com)

Stanislav Moiseev (spmoiseev@gmail.com)

Georgy Mkrtchyan (gnmkrtchyan@gmail.com)

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