Social Networks: Theory and Applications

1
Social Networks Theory and Applications
Yong Tan Michael G. Foster School of
Business University of Washington
A Tutorial Presented at INFORMS Annual Meeting,
Seattle, November 7, 2007
2
Acknowledgements

• Ted Klastorin (Tutorials Chair)
• Param Vir Singh
• V. Mookerjee, D. Dey, M. Fan, C. Phelps, A.
  Susarla, A. Jain, G. Zhang, J. Oh, Y. Lee, L.
  Yan, N. Yu, D. Choi, A. Ozler

3
Outline

• Introduction
• Economic Approach
• Random Graph
• Social Network Analysis
• Social Capital
• Data Collection
• Software
• Selected Applications

4
What Is Social Network

• A map of relationships (formal or informal) among
  actors (person, organization, and others)
• Representations
• Graph
• Matrix (Sociomatrix)

5
Friend Network

• Oh, Susarla, and Tan 2007

6
Subscriber Network

• Oh, Susarla, and Tan 2007

7
OSS Collaboration Network

• Singh, Tan, and Mookerjee 2007

8
Blogs

• Zhang and Tan 2007

9
Why Is It Important?

• Our research focus on economic factors
• Social embeddedness Granovetter (1985)
• Economic actions are embedded in concrete,
  ongoing systems of social relations
• Networks are central
• Resource sharing, information dissemination, and
  knowledge spillover
• White collar workforce management
• Wally Hopp et al
• Successful business models
• MySpace, FaceBook, YouTube,

10
It Is Getting Popular!

• Phelps, Singh and Heidl

11
I. Economic and Social Networks Stability and
Efficiency

• Networks and Groups Models of Strategic
  Formation. B. Dutta and M.O. Jackson eds, 2003.

12
Introduction

• Both economic and social interactions involve
  network relationships
• The specifics of the network structure are
  important in determining the outcome
• The aims are to
• develop a systematic analysis of how incentives
  of individuals affect the formation of networks
• align with social efficiency

13
Definitions

• A set N 1,?,n of individuals are connected in
  a network relationship.
• Individuals are the nodes in the graph and links
  indicate relationships between the individuals
• Bilateral relationship ? Non-directed Networks
• Marriage, friendship, alliances, exchange, etc.
• Both parties should consent to form a link
• Unilateral relationships ? Directed Networks
• Advertising or links to web sites etc.

14
Notations

• ij represents the link i, j
• ij ? g indicates that i and j are linked under
  network g
• G g ? gN denotes the set of all possible
  networks or graphs on N, with gN being the
  complete network
• g ij network obtained by adding link ij to an
  existing network g
• g - ij network obtained by deleting link ij to
  an existing network g
• N(g)i ?j s.t. ij ? g set of individuals who
  have at least one link in network g

15
Paths and Components

• Given a network g ? G, a path in g between i and
  j is a sequence of individuals i1,i2,,iK such
  that ikik1 ? g for each k ? 1,, K - 1, with
  i1 i and iK j.

• A (connected) component of a network g, is a
  nonempty subnetwork g? g, such that
• if i ? N(g) and j ? N(g) where j ? i, then
  there exists a path in g between i and j
• if i ? N(g) and j ? N(g) where j ? i, then
  there does not exist a path in g between i and j
• The set of components of g is denoted C(g) and g
  ?g?C(g)g

16
Value Functions

• Different network configurations lead to
  different values of overall production or overall
  utility to a society. These possible valuations
  are represented via a value function.
• The set of all possible value functions is
  denoted V
• Different networks that connect the same
  individuals may lead to different values
• Value function can incorporate costs to links as
  well as benefits

17
Allocation Rules

• A value function keeps track of how the total
  societal value varies across different networks
• An allocation rule
• is used to keep track of how that value is
  distributed among the individuals forming a
  network
• is a function Y G ?V ? RN such that ?iYi(g, v)
  v(g) for all v and g
• depends on both g and v. This allows an
  allocation rule to take full account of an
  individual is role in the network

18
Pareto Efficiency

• A network g is Pareto efficient relative to v and
  Y if there does not exist any g?G such that
  Yi(g,v) ? Yi(g,v) for all i with strict
  inequality for some i.
• This definition of efficiency of a network takes
  Y as fixed, and hence can be thought of as
  applying to situations where no intervention is
  possible

19
Efficiency

• A network g is efficient relative to v if v(g) ?
  v(g) for all g?G.
• This is a strong notion of efficiency as it takes
  the perspective that value is fully transferrable
• Unlimited intervention is possible
• g is efficient relative to v if g is PE relative
  to v and Y for all Y

20
Pairwise Stability

• A network g is pairwise stable with respect to
  allocation rule Y and value function v if
• A network is pairwise stable if it is not
  defeated by another (necessarily adjacent)
  network
• It is a weak notion as it considers only
  deviations on a single link at a time and only
  deviations by at most a pair of individuals at a
  time
• It is not a sufficient requirement for a network
  to be stable over time.

21
Existence of Pairwise Stable Networks

• In some situations, there may not exist any
  pairwise stable network. Each network is defeated
  by some adjacent network, and that these
  improving paths form cycles with no undefeated
  networks existing
• An improving path is a sequence of networks g1,
  g2, , gK where each network gk is defeated by
  the subsequent (adjacent) network gk1.

22
Example Exchange Networks
7/96
7/96
23
Compatibility of Efficiency and Stability

• While there are situations where the allocation
  rule is an object of design, we are also
  interested in understanding when naturally
  arising allocation rules lead to pairwise stable
  networks that are (Pareto) efficient.
• Example Coauthor Model Each individual is a
  researcher who spends time working on research
  projects. If two are connected, they are working
  on a project together. The amount of time
  researcher i spends on a given project is
  inversely related to the number of projects, ni.
  is payoff is
• For n 4, the complete network is pairwise
  stable with payoff of 2.5 for each player. For
  network g 12,34, each individual have payoff
  of 3. So the unique pairwise stable network is
  Pareto inefficient.

24
Dynamic Model of Network Formation

• Since network structure affects economic
  outcomes, it is crucial to know which network
  configurations will arise
• Process of network formation in a dynamic
  framework is analyzed
• Formation process is found to be path dependent,
  thus the process often converges to an
  inefficient network structure

25
Static Model

• Connection Model (Jackson and Wolinsky)
• There are n agents, N 1,2, ,n, are able to
  communicate each other
• Each agent i ?1, ,n receives a payoff ui(g),
  from the network g
• i receives a payoff of 1 ? 0 for each direct
  link he has
• i pays a cost c 0 of maintaining each direct
  link he has
• t(ij) number of direct links in the shortest
  path between agent i and j (i ? j). ?t(ij) is the
  payoff agent i receives from being indirectly
  connected to agent j

26
Static Model Results

• For all N, a stable network exists. Further,
• if c ?2, then gN is stable
  (unique)
• if c ? ?, then the empty network is stable (not
  usually unique)
• if c stable (not usually unique)
• For all N, a unique efficient network exists.
  Further,
• if ? - c ?2, then gN is the efficient network
• if ? - c ?2 and , then
  a star network is efficient
• if ? - c ?2 and , then
  the empty network is efficient

27
Dynamic Model

• Initially n players are unconnected
• Players meet over time and have opportunity to
  form links with each other
• Time, T, is divided into countable, infinite set,
  T 1,2, ,t,
• gt network exists at the end of period t
• ui(gt) payoff of player i at the end of period t
• In each period, a link ij is randomly identified
  to be updated with uniform probability
• If ij ? gt-1, either i or j can decide to sever
  the link
• If ij ? gt-1, players i and j can form a link ij
  and simultaneously sever any of their other
  links if both agree
• Each player is myopic
• If after some time period t, no additional links
  are formed or broken, then the network formation
  has reached a stable state

28
Dynamic Network Formation Results

• If ? - c ?2 0, then every link forms (ASAP)
  and remains (no links are ever broken). If ? - c
  
• If player i and j are not directly connected,
  they will each gain at least (? - c) - ?t(ij) 0
  from forming a direct link. If ?
  - c ?2 0, connection will take place.
• If ? - c ?2 0, formation converges to gN
  (unique efficient and stable network)
• If ? - c j, then each agent will receive a payoff ? - c 0. Since agents are myopic, they will refuse to
  link
• If ? - c It is efficient iff

29
II. Random Graphs

• The Structure and Dynamics of Networks. M.
  Newman, A. Barabasi, and D.J. Watts eds,
  2006.Handbook of Graphs and Networks From the
  Genome to the Internet. S. Bornholdt and H.G.
  Schuster eds, 2003.Random Graphs Dynamics. R.
  Durrett, 2007Complex Social Networks. F.
  Vega-Redondo, 2007

30
Review and Background

• Network graph
• Vertex (node, site)
• Edge (link, bond)
• graph (network) is
• a pair of sets G V, E
• V is a set of N nodes (vertices)
• E is a set of edges connecting elements of V
• Edges do not have length (except in metric
  spaces)

31
Network Models

• Random graphs
• Taking n dots and drawing nz/2 lines between
  random pairs
• Completely ordered lattice
• A low dimension regular lattice
• Watts-Strogatz model (Small-world)
• A low dimension regular lattice with some degrees
  of randomness
• Barabasi-Albert model (Scale-free)

32
Properties

• Degree of a vertex is a number of edges attached
  to it (if directed incoming and outgoing
  degree)
• Geodesic path the shortest path from one node
  to another (measured in nodes)
• Diameter of the network the longest geodesic
  path between any two vertices (not mean)
• Average geodesic path length

33
Random Graphs

• Studied by P. Erdös A. Rényi in 1960s
• How to build a random graph
• Take n vertices
• Connect each pair of vertices with an edge with
  some probability p
• There are n(n-1)/2 possible edges
• The mean number of edges per vertex is

34
Degree Distribution

• Probability that a vertex of has degree k follows
  binomial distribution
• In the limit of n kz, Poisson distribution
• z is the mean

35
Characteristics

• Small-world effect (Milgram 60s)
• Diameter (Bollobas)
• Average vertex-vertex distance
• Grows slowly (logarithmically with the size)
• Some inaccuracies describing real-world networks
• Degree distribution (not Poisson!)
• Clustering (Network transitivity)
• If A and B have a common friend C it is more
  likely that they themselves will be friends.
• Random graph z / n
• social networks, biological networks in nature,
  artificial networks power grid, WWW ranging
  from 0.08 to 0.59

36
Clustering

• If A is connected to B, and B is connected to C,
  then it is likely that A is connected to C
• A friend of your friend is your friend
• The average fraction of a nodes neighbor pairs
  that are also neighbors each other
• Count up the total number of pairs of vertices on
  the entire graph that have a common neighbor and
  the total number of such pairs that are also
  themselves connected, and divide the one by the
  other

37
Small-World Model

• Watts-Strogatz (1998) first introduced small
  world mode
• connects regular and random networks
• Regular Graphs have a high clustering
  coefficient, but also a high diameter
• Random Graphs have a low clustering coefficient,
  but a low diameter
• Characteristic of the small-world model
• The length of the shortest chain connecting two
  vertices grow very slowly, i.e., in general
  logarithmically, with the size of the network
• Higher clustering or network transitivity

38
Scale-Free Network

• A small proportion of the nodes in a scale-free
  network have high degree of connection
• Power law distribution
• A given node has k connections to other nodes
  with probability as the power law distribution
  with exponent ? 2, 3
• Examples of known scale-free networks
• Communication Network - Internet
• Ecosystems and Cellular Systems
• Social network responsible for spread of disease

39
Scale-Free Network
Linked The New Science of Networks by
Albert-Laszlo Barabasi
40
Barabasi-Albert Networks

• Science 286 (1999)
• Start from a small number of node, add a new node
  with m links
• Preferential Attachment
• Probability of these links to connect to existing
  nodes is proportional to the nodes degree
• Rich gets richer
• This creates hubs few nodes with very large
  degrees

41
Analysis
ti time vertex i is added
42
Scale-free Networks Good and Bad

• Scale-free networks cannot be broken by random
  node removal
• Attacks can bring them down hackers attacks,
  major servers (DNS) downed by a computer virus
• In scale-free networks there is no epidemic
  threshold any outbreak should become an epidemic
• Berger et al, On the spread of viruses on the
  Internet, Proceedings of the 16th annual ACMSIAM
  symposium, 2005

43
III. Social Networks Analysis (SNA)

• Social Network Analysis Methods and
  Applications. S. Wasserman and K. Faust,
  1994.Models and Methods of Social Network
  Analysis. P.J. Carrington, J, Scott, and S.
  Wasserman eds, 2005.

44
3.1 Centrality and Prestige
45
Prominence

• The identification of the most important actors
  in a social network
• A variety of measures actor location in a
  social network
• (Degree, Closeness, Betweenness, Information,
  Rank)
• Quantifying measures
• Actor indices as the prominence in a network
• Group-level index Aggregation across actors
• Relations directional and non-directional
• Centrality dichotomous relations
• Prestige choices received

46
Centrality and Prestige

• Prominent actors are those that are extensively
  involved in relationships with other actors
• The focus of involvement
• A central actor as one involved in many ties
• Most appropriate for non-directional relations
• The difference between the source and the
  receiver is less important than just
  participating in many interactions
• Most access or most control or who are the most
  active brokers
• A prestigious actor as one who is the object of
  extensive ties
• Focusing solely on the actor as a recipient
• The relational is directional In-degrees are
  only distinguishable from out-degree for
  directional relations

47
Degree Centrality

• The simplest definition The most ties to other
  actors in the network
• Focuses only on direct or adjacent choices
• Actor Degree Centrality
• An actor with a large degree is in direct contact
  or is adjacent to many other actors
• This actor should then begin to be recognized by
  others as a major channel of relational
  information

48
Degree Centrality

• Group Degree Centralization
• The index is also a measure of the dispersion of
  the actor indices, since it compares each actor
  index to the maximum attained value
• Standard statistical summary of the actor degree
  indices is the variance of the degrees

49
Three Illustrative Networks
(a) Star Graph
(b) Circle Graph
(c) Line Graph
50
Eigenvector Centrality

• Importance of an actor in a network
• Sociomatrix (Adjacency matrix)
• Aij 1, if a link between i and j 0 otherwise
• Centrality measure xi
• In matrix form
• Here l is the eigenvalue

Degree Centrality
51
Closeness Centrality

• The measure focuses on how close an actor is to
  all the other actors in the set of actors
• An actor is central if it can quickly interact
  with all others
• The geodesics, or shortest paths minimum
  distance
• Actor Closeness Centrality a function of
  geodesic distances
• depends not only on direct ties but also on
  indirect ties

52
Closeness Centrality

• Group Closeness Centralization
• The variance of the standardized actor closeness
  indices
• Standard statistical summary of the actor degree
  indices is the variance of the closeness

53
Three Illustrative Networks
(a) Star Graph
(b) Circle Graph
(c) Line Graph
54
Betweenness Centrality

• Interactions between two non-adjacent actors
  might depend on the other actors in the set of
  actors, especially the actors who lie on the
  paths between the two nodes
• Actor in the middle between the others has some
  control over paths in the graph interpersonal
  influence
• The probability that a communication, or a path
  from j to k takes a particular route critical
  assumption lines have equal weight

55
Betweenness Centrality

• Actor Betweenness Centrality All geodesics are
  equally likely to be used

56
Three Illustrative Networks
(a) Star Graph
(b) Circle Graph
(c) Line Graph
57
Directional Relations

• Centrality indices for directional relations
  generally focus on choices made, while prestige
  indices generally examine choices received, both
  direct and indirect
• Centrality (Degree and Closeness)
• Prestige

58
Degree Prestige

• The simplest actor-level measure of prestige
  (in-degree)
• The idea is that actors who are prestigious tend
  to receive many nominations or choices

59
Proximity Prestige

• Degree prestige only counts actors who are
  adjacent to actor i
• Influence domain of actor i Reachability
• the set of actors who are both directly and
  indirectly linked to actor j
• consists of all actors whose entries in the j-th
  column of the distance matrix or the reachability
  matrix
• Example

Influence domain of actor 3
3
2
1
4
60
Proximity Prestige

• How proximate the actor is to the actors in its
  influence domain
• Proximity as closeness in its influence domain
• Number of actors in actor is influence domain
• The average distance
• The fraction of the actors in the set of actors
  who can reach an actor
• As actors who can reach i become closer, on
  average, then the ratio becomes larger

61
Group Centrality
Group1
Group 2

• In both groups, actors have degree 4
• In Group1, the pair are structurally equivalent
• In Group 2, the pair are adjacent to four
  different actors
• Simple aggregation results in the same
  centrality, however, the Group 2 should be a
  better score

62
3.2 Structural EquivalenceNetwork Position and
Role
63
Social Roles and Positions

• Position
• A collection of individuals who are similarly
  embedded in networks of relations (ex. in social
  activity, ties, or intersections, with regard to
  actors in other positions)
• This concept is quite different from the concept
  of cohesive subgroup (Why? based on the
  similarity of ties rather than their adjacency,
  proximity, or reachability.)
• Example
• Nurses in different hospitals occupy the position
  of nurse though individual nurses may not know
  each other, work with the same doctors, or see
  the same patients

64
Social Roles and Positions

• Role
• The patterns of relations which obtain between
  actors or between positions
• An associations among relations that link social
  positions
• Collections of relations and the associations
  among relations
• Example
• Kinship roles
• Defined in terms of combinations of the relations
  of marriage and descent
• Roles of corporate organization
• Defined in terms of levels in a chain of command
  or authority

65
Definition of Structural Equivalence

• Actor i and j are structurally equivalent if
  actor i has a tie to k, iff j also has a tie to
  k, and i has a tie from k iff j also has a tie
  from k.

66
Structural Equivalence

• Example (Sociomatrix and directed graph)

Both have ties to 3 and 4
Both have ties to 5
Directed graph
Sociomatrix
3 subsets of structural equivalent actors ? B1
1,2, B2 3,4, B3 5
67
Positional Analysis
Sociomatrix
Permuted and partitioned sociomatrix
Image matrix

• Three subsets of structural equivalent actors
• B1 6,3,8, B2 2,5,7, B3 4,1,9

68
Position Analysis
Graph (from the partitioned sociomatrix)
Reduced Graph (from the image matrix)
5
B3
B1
1
7
2
B2
9
4
3
8
B2
B3
6
B1
69
Position Analysis - Measures

• Euclidean Distance
• Single relation
• Multiple relation

The value of the tie from i to k on a single
relation
The value of the tie from i to k on relation
Sum of the size of relations
70
Position Analysis - Measures

• Correlation (Pearson product-moment)
• Single relation
• Multiple relation

The mean of the values in column i
The mean of the values in row i
71
3.3 Cohesive SubgroupsAffiliation Networks
72
Background

• Cohesive subgroups are subsets of actors among
  whom there are relatively strong, direct,
  intense, frequent, or positive ties.
• Although the literature contains numerous ways to
  conceptualize the idea of subgroup, there are
  four general properties
• The mutuality of ties
• The closeness of reachability of subgroup members
• The frequency of ties among members
• The relative frequency of ties among subgroup
  members compared to non-members

73
Subgroups Based on Complete Mutuality

• Cliquish subgroups (Festinger and Luce and
  Perry)
• Cohesive subgroups in directional dichotomous
  relations would be characterized by sets of
  people among whom all friendship choices were
  mutual.
• Definition of a Clique
• A clique in a graph is a maximal complete
  subgraph of three or more nodes, all of which are
  adjacent to each other, and there are no other
  nodes that are also adjacent to all of the
  members of the clique.

74
Subgroups Based on Complete Mutuality

• Example
• Cliques 1,2,3,1,3,5, and 3,4,5,6

7
2
3
1
4
6
5
75
Subgroups Based on Reachability and Diameter

• n-cliques
• An n-clique is a maximal subgraph in which the
  largest geodesic distance between any two nodes
  is no greater than n.
• n-clans
• An n-clan is an n-clique, in which the
  geodesic distance, d(i,j), between all nodes in
  the subgraph is no greater than n for paths
  within the subgraph
• n-clubs
• An n-club is defined as a maximal subgraph of
  diameter n.

76
Subgroups Based on Reachability and Diameter

• Example
• 2-cliques
• 1,2,3,4,5 2,3,4,5,6
• 2-clans
• 2,3,4,5,6
• 2-clubs
• 1,2,3,4 1,2,3,5
• 2,3,4,5,6

1
2
3
5
4
6
77
Measures of Subgroup Cohesion

• A measure of degree to which strong ties are
  within rather than outside is given by the ratio

• The numerator is the average strength of the ties
  within and the denominator is the average
  strength from subgroup members to outsiders

78
Affiliation Networks

• Affiliation networks are two-mode networks
• Affiliation networks consist of subsets of
  actors, rather than simply pairs of actors
• Connections among members of one of the modes are
  based on linkages established through the second
  mode
• Affiliation networks allow one to study the dual
  perspectives of the actors and the events

79
Collaboration Network
80
IV. SOCIAL CAPITAL

• Structural Holes The Social Structure of
  Competition. R.S. Burt, 1995.

81
Why Is Social Capital Important?

• Using an example of OSS
• OSS is developed by voluntary developers through
  individual incremental efforts and collaboration.
  
• New contributions to the code often involve, to a
  large extent, a recombination of known conceptual
  and physical materials (Narduzzo and Rossi 2003,
  Fleming 2001).
• Developers with better access to and familiarity
  of such materials are advantaged in their code
  development efforts.
• Because information about and knowledge of
  resources often lies spread across developers in
  the community, social capital, i.e. a developers
  access to resources from a network of
  relationships, may emerge as a key factor that
  differentiates those who are more productive than
  others.

82
Network Relationships and Knowledge Benefits

• Relationships among developers in a network
  provide them with two types of knowledge benefits
  resource sharing and knowledge spillovers.
• Resource sharing allows them to combine know-how
  and physical assets
• Knowledge spillovers provide information about
  current design problems, failed approaches, new
  breakthroughs, and opportunities.

83
Network Elements Direct Ties

• Developers who work together on a project share
  direct ties with each other.
• These ties provide opportunities for repeat,
  intense interactions and are conducive for
  resource sharing as well as knowledge spillover.
• The knowledge acquisition depends on knowing who
  knows what and developers with large number of
  direct ties are likely to be privy to such
  information.

84
Network Elements Indirect Ties

• Indirect relationships (where two developers do
  not work together but can be reached through
  mutual acquaintances) are less likely to provide
  opportunities for repeat interactions and, hence,
  are not conducive to resource sharing. However,
  knowledge spillovers do not require repeat
  interactions and, hence, indirect relationships
  will be conducive to them.
• Developers in a relationship also bring with them
  the knowledge and experience from their
  interactions with other partners. Hence, a
  developers relationship with another developer
  provides it with access to not just its own
  partners but to its partners partners.

85
Network Elements Network Cohesion

• Cohesiveness means that ties are redundant
• To the degree that they lead back to the same
  actors
• Such redundancy increases the information
  transmission capacity in a group of developers
  having cohesive ties
• It promotes sharing and makes information
  exchange
• Speedy
• Reliable
• Effective
• Information between two developers in a cohesive
  group can flow through multiple pathways this
  increases the speed as well as reliability of
  information transfer.

86
Network Cohesion (2)

• Cohesiveness in the group
• gives rise to trust, reciprocity norms, and a
  shared identity
• leads to a high level of cooperation
• facilitate collaboration by providing
  self-enforcing informal governance mechanisms
• Cohesive ties enable richer and greater amounts
  of information and knowledge to be reliably
  exchanged
• The groups also provide meaningful context for
  information and resource sharing
• The trust among the members in the group affords
  them to be creative
• This creativity helps in coming up with
  alternative interpretation of current problems,
  or novel approaches to solve these problems

87
Network Elements Structural Hole

• Cohesion
• Lead to norms of adhering to established
  standards and conventions
• Potentially stifle innovation
• The standards, conventions and knowledge stocks
  vary across groups.
• Structural holes are the gaps in the information
  flow between these groups.
• Developers who connect different groups are said
  to fill these structural holes.
• Teams composed of developers who span different
  groups may have several advantages.

88
Illustrative Partial Developer Network

• Developers are represented by spheres and color
  coded by component.
• An arc joining two developers indicates the
  existence of a direct tie between them.
• The developer indicated spanning the structural
  hole connects the two groups of developers which
  have cohesive ties within each group.
• Project teams that would include the indicated
  developer will have direct access to the
  knowledge resources of the two groups.

89
Structural Hole (2)

• Teams composed of developers who span different
  groups may have several advantages.
• Technical or organizational problems and
  difficulties of a developer in one group can be
  easily and reliably relayed to developers in
  other groups. The solutions for these problems
  may be obvious to someone and would be quickly
  and reliably relayed back.
• Each group has its own best practices
  (organizational or technical perspectives) which
  may have value for other groups. The developers
  who connect these groups can see how resources or
  practices in one may create value for other and
  synthesize, translate as well as transfer them
  across groups.
• Resource pooling across groups provide developers
  opportunities to work on different but related
  problem domains, which may help them in
  developing a better understanding of their own
  problems.

90
Structural Hole vs Network Closure

• These two arguments promote two contradicting
  predictions.
• The network cohesion argument predicts that teams
  formed of developers who share cohesive ties will
  be more successful due to better coordination and
  communication resulting from increased
  information transmission capacity.
• The structural holes argument predicts that teams
  formed of developers who span structural holes
  will be more successful due to access to wider
  range of knowledge resources.

91
Measures

• Direct Ties
• Indirect Ties (Burt 1992)
• n total number of developers in the network
• wij number of developers that lie at a path
  length of j from i
• zij decay associated with the information that
  is received from developers at path length j
• fij number of developers that i can reach within
  and including path length j
• Ni total number of developers that i can reach
  in the network

92
Measures (2)

• Network Closure or Structural Hole (Burt 1992)
• Network Cohesion is indirect structural
  constraint
• Computed as
• Where
• Mi ? number of direct ties for developer i
• piq ? proportion of is relations invested in the
  relationship with j

93
Social Capital and OSS Success

• Singh, Tan, and Mookerjee (2007)
• Data
• 5191 projects and 10973 developers

94
Data Collection

• The challenge is determining network boundary
• Two approaches
• Whole network
• Not easy
• Ego-centric
• Problematic
• Snowballing

95
Software

• UCINET
• Software for Social Network Analysis (Borgatti,
  Everett, and Freeman)
• Pajek
• R
• SNA module
• StOCNET
• SIENA module
• Longitudinal data (Snijders 2004)
• Dynamic network
• MCMC

96
SELECTED APPLICATIONS
97
Strategy and Organization

• Firm alliance (RD) network
• Board of director network
• Venture capital network
• Team social network

98
Marketing

• Social contagion
• Estimating customer value
• Gupta et al (2006)
• Social Network and Marketing
• Ven den Bulte and Wuyts (2007)

99
Information Systems

• Open Source Software Development Collaboration
  Network
• Singh (2007)
• Singh, Tan, and Mookerjee (2007)
• Online Communities
• Productivity, Information
• Aral and Van Alstyne (2007)
• Aral, Brynjolfsson and Van Alstyne (2007)

100
Finance

• Financial Networks
• Leinter (2005)
• Venture Capital Networks and Investment
  Performance
• Hochberg et al (2007)

101
Thank You!