What are social networks?

• The set of (exchange) relationships between people or other social units.

• A directed graph, with people, groups, or organizations as the nodes and the entities exchanged as the link

• Vary in size, density, clumpiness

• Some types of networks

• Communication

• Advice/information

• Friendship

• Trust/social support

• Tangible exchange/Material support

• Similarity

• Structure matters

• Clique• Isolates• Stars• Boundary spanners

Types of Relationships Among People

Why are they important?• Actors who are connected, influence each other• “Goods” (e.g., info, opportunities, power) flow through

networks

• Actors’ position in the network influence their success• Good managers/researchers cultivate extensive

networks, inside & outside the organization at all levels

Social Capital

• Capital– A resource that can be accumulated– Availability allows people to create more value for self

or others

• Physical capital (vs. labor)– E.g., Factories, tools, computers

• Human capital– E.g., Training, education

• Social capital– E.g., Friendships, trust, common identity

Social Capital

• The extra resources that people get by being connected to others– Analogous to physical capital (e.g., factory

automation)– Human capital (e.g., college education)

• Social capital benefits– Individual – increased health & happiness– Communities – reduced corruption

Effects of Social Capital

• Social capital is correlated with positive individual and collective outcome– Better health– Lower crime– Better educational outcomes– Good government

• Age-adjusted relative risk of dying among those lacking social contact during a 9-year period (Berkman, 1983)

• Sources of social support• Being married  • Frequent contact with family

and close friends • Active member of a church • Active participation in a club

or other social group

Social Support Health & Happiness

Strength of ties

• Strong ties (Krackhard)– Intimacy, self-disclosure, provide support– Feel close w/frequent contact– Spouse, relatives, close friends

• Weak ties (Granovetter)– Diverse resources, broader base– Feel distance w/infrequent contact– Acquaintances, colleagues from elsewhere

• Strong tie = “close relationship/friend”• Social relationship with high frequency, emotional

commitment, multiplicity (overlap), and reciprocity• Strong ties tend to know same things & people• Strong ties tend to fill in the gaps (e.g., friends of

friends become friends; friends tend to share taste)

• Strong ties useful for– Money– Advice– Arduous help– Friendship

Nature of the Social Tie Matters

• Weak tie = “weak relationship/causal acquaintance” • Social relationships with low frequency, intensity, breadth, and

reciprocity (Granovetter: Strength of Weak Ties)

• Hypothesis: Weak ties lead to more extensive and diverse social networks, and are more likely to overcome gaps of class, race, and other sources of division

• Data: Job changers get their jobs through weak ties: e.g.. only 16% from contacts they see weekly and 28% they see less than yearly

• Weak ties useful for – New information– Finding jobs

Nature of the Social Tie Matters

Strong vs Weak Ties Online

• Random assignment experiment to test info flow thru strong vs weak tie

• DV: Probability of friend posting the link• N: ~ 400M Facebook users

With link in feed Without link in feed

Bakshy, E., Rosenn, I., Marlow, C., & Adamic, L. (2012). The role of social networks in information diffusion Proceedings of the 21st international conference on World Wide Web. (pp. 519-528). NY:: ACM.

Feed subjects share more

• Subjects in feed condition were more likely to share– Feed: .191% shared– No feed: .025% shared– Increase = 7.37x

• Shared fasted• More exposure leads to

more sharing

Which friends lead to more sharing?

• 4 indices of tie strength

Influence of Strong vs Weak Ties

• Strong Ties Are More Influential per capita

• But effect of tie strength is even higher in no feed condition redundancy

Overall Influence of Strong vs Weak Ties

Why are they important?

• Examining social networks can help diagnose organizational problems– find informational bottlenecks/distribution channels– select successful team leaders and managers

• Good managers understand that there are both formal and

informal networks in an organization

Examples: Interdisciplinary collaboration

Stunning Density ComparisonArchitecture BHA/BSA:

Race & school friendships

Moody, Jame (2002) Race, School Integration, and Friendship Segregation in America. The American journal of sociology [0002-9602] Moody yr:2002 vol:107 iss:3 pg:679

Familiarity in a CMU Project Class

79% non-Asian

83% Asian

Bloggers X Party

Measures of Centrality

37

Degree

Betweenness

Closeness

Eigenvector

How many people can this person reach directly?

How likely is this person to be the most direct route between two people in the network?

How fast can this person reach everyone in the network?

How well is this person connected to other well-connected people?

Centrality measure Interpretation in social networks

Degree centrality• A node’s (in-) or (out-)degree is the

number of links that lead into or out of the node

• In an undirected graph they are of course identical

• Often used as measure of a node’s degree of connectedness and hence also influence and/or popularity

• Useful in assessing which nodes are central with respect to spreading information and influencing others in their immediate ‘neighborhood’

38

12

3

45

67

2

3

4

14

11

Nodes 3 and 5 have the highest degree (4)

Hypothetical graph

Betweenness centrality For a given node v, calculate the

number of shortest paths between nodes i and j that pass through v, and divide by all shortest paths between nodes i and j

Sum the above values for all node pairs i,j

Sometimes normalized such that the highest value is 1or that the sum of all betweenness centralities in the network is 1

Shows which nodes are more likely to be in communication paths between other nodes

Also useful in determining points where the network would break apart (think who would be cut off if nodes 3 or 5 would disappear)

39

12

3

45

67

0

1.5

6.5

09

00

Node 5 has higher betweenness centrality than 3

Closeness centrality• Calculate the mean length of all

shortest paths from a node to all other nodes in the network (i.e. how many hops on average it takes to reach every other node)

• Take the reciprocal of the above value so that higher values are ‘better’ (indicate higher closeness) like in other measures of centrality

• It is a measure of reach, i.e. the speed with which information can reach other nodes from a given starting node

40

12

3

45

67

0.5

0.67

0.75

0.460.75

0.460.46

Nodes 3 and 5 have the highest (i.e. best) closeness, while node 2 fares almost as well Note: Sometimes closeness is calculated without taking the reciprocal

of the mean shortest path length. Then lower values are ‘better’.

Eigenvector centrality• A node’s eigenvector centrality is

proportional to the sum of the eigenvector centralities of all nodes directly connected to it

• In other words, a node with a high eigenvector centrality is connected to other nodes with high eigenvector centrality

• This is similar to how Google ranks web pages: links from highly linked-to pages count more

• Useful in determining who is connected to the most connected nodes

CNM Social Media Module – Giorgos Cheliotis (gcheliotis@nus.edu.sg)

41

12

3

45

67

0.36

0.49

0.54

0.190.49

0.170.17

Node 3 has the highest eigenvector centrality, closely followed by 2 and 5

Note: The term ‘eigenvector’ comes from mathematics (matrix algebra), but it is not necessary for understanding how to interpret this measure

Values computed with the sna package in the R programming environment. Definitions of centrality measures may vary slightly in other software.

Basic Concepts

Networks

Tie Strength

Key Players Cohesion

44

How to represent various social networks

How to identify strong/weak ties in the network

How to identify key/central nodes in network

How to characterize a network’s structure

Social Capital

Density

47

12

34

• A network’s density is the ratio of the number of edges in the network over the total number of possible edges between all pairs of nodes (which is n(n-1)/2, where n is the number of vertices, for an undirected graph)

• In the example network to the right density=5/6=0.83 (i.e. it is a fairly dense network; opposite would be a sparse network)

• It is a common measure of how well connected a network is (in other words, how closely knit it is) – a perfectly connected network is called a clique and has density=1

• A directed graph will have half the density of its undirected equivalent, because there are twice as many possible edges, i.e. n(n-1)

• Density is useful in comparing networks against each other, or in doing the same for different regions within a single network

12

34

density = 5/6 = 0.83

density = 5/12 = 0.42

Edge present in network

Possible but not present

Dense Social Networks Are Good for the Group (Coleman, 1990)

• Dense networks are useful at the organizational level

• Provide– Information & other resources– Trust thru effects of reputation

Who Helps Whom with the Rice Harvest?

Which Village Is More Likely to Survive?

Social Capital

• Investment in time, energy and other resources in individual and organized social relationships

• Relationships have benefits – Knowledge, innovation, resources– Individual health and happiness– Community efficiency, safety and quality

Groups rely upon networks for

success• Allen: Bring technical knowledge into R&D teams

• Coleman: Rapid adoption of medical innovations among community of MDs

• Curtis: Software engineering

• Getting application domain requirements

• Keeping up with changing environment of use and development

• Ancona: New product development teams

• Convince the boss

• Get the support of "sister" departments

Allen-Gatekeepers• Gatekeepers moderate the flow of technical

information into R&D groups– Connected both within and outside the group– Technically competent & often a supervisor

Allen-Gatekeepers• Groups rely on this network structure to bring

new knowledge into the system

Outside connections improve performance evaulations

Cross, R & Cummings, J. (2004) Tie and network correlates of individual performance in knowledge intensive work Academy of Management Journal, 47(6), 928.

Clustering

58

12

3

45

67

1

0.67

0.33

N/a

0.17

N/aN/a

• A node’s clustering coefficient is the number of closed triplets in the node’s neighborhood over the total number of triplets in the neighborhood. It is also known as transitivity.

• E.g., node 1 to the right has a value of 1 because it is only connected to 2 and 3, and these nodes are also connected to one another (i.e. the only triplet in the neighborhood of 1 is closed). We say that nodes 1,2, and 3 form a clique.

• Clustering algorithms identify clusters or ‘communities’ within networks based on network structure and specific clustering criteria (example shown to the right with two clusters is based on edge betweenness, an equivalent for edges of the betweenness centrality presented earlier for nodes)

Network clustering coefficient = 0.375 (3 nodes in each triangle x 2 triangles = 6 closed triplets divided by 16 total)

Cluster A

Cluster B

Values computed with the igraph package in the R programming environment. Definitions of centrality measures may vary slightly in other software.

Structural Holes

• Network closure – relations are embedded in a network– Enhance group identification– Foster exchange of ideas

• Structural holes – relations bridge disconnected networks– Access to unique information– Broker third parties

Structural holes – benefits• A structural hole exists when there is only a

weak connection between two dense clusters– Control benefits:

• brokers control the interaction between two network components

– Information benefits: • brokers have access to unique information, this makes them

invaluable

• Structural holes are a competitive advantage– Separate non-redundant sources of information– Information from different sources is more additive

than overlapping

Advantages of Structural Holes (Burt, 2000)

Zoom in on a cluster

Extras

The small world problemThe small world problem: the hypothesis that everyone in the world can be reached through a short chain of social ties.

•Size of personal networks:– Weak ties: ~280 persons known– Strong ties: 6-30

•Networks are generally sparse– Most of one’s ties don’t know each other

•Strong ties useful for– Advice– Arduous help– Friendship

•Weak ties useful for – New information

Estimated Network Size

• Bernard & Killworth

http://www.analytictech.com/connections/v20(1)/keynote.htm

•Social networks are potentially unbounded•People have large personal networks

• ~30 in local social circle = in Pgh and monthly communication• ~40 in distant social circle = outside Pgh and yearly communication

• Maximum number of contacts at 5 removed from self: 705 ~ 1.7 billion

•Milgram: What is the actual path between any two people in the world

• Give a document to someone you know personally, who will get it closer

to its target• ~ 22% of attempts complete

• Completed chains ~5 people long• Completion rates are lower & lengths are longer if chain has to pass

race, geography, or occupational lines• Selection of next person is biased toward a similar others (local, class

& gender)

Six degrees of separation

Small world – results

• Common channels:– 16 (25%) reached the target through the

same neighbor– 10 reached the target through one business

associate, 5 through another

• Nearly 50% of the letters reached the target through 3 channels!– “social stars” – high degree and betweenness

centrality!Small World Project - Columbia University The Electronic Small World Project

Monge & Contractor

• Attempt to classify types of social network theories

• Endogenous Variables – Capture the extent to which relational

properties of the network influence self-organization

• Exogenous Variables– Refer to various properties outside the focal

network that influence the probability ties will be present or absent in the focal network

Testing Multilevel, Multitheoretical Hypothesis about Organizational

NetworksContractor, Wasserman, and Faust

Select Social Theories

Multilevel, Multitheoretical Frameworkpresented by Contractor, Wasserman, and Faust

Level

Actor Dyadic Triadic Global Other Time

Endogenous

actor structural autonomy

mutuality,reciprocatio

n

transitivity, cyclicality

network centralizatio

n

Exogenousage,

gender, org type, education

differential mutuality

and reciprocatio

n

differential transitivity

and cyclicality

differential network

centralization

advice, friendshi

p network

communication network

Link Communication & Closeness X Relationship Type

Groups in an organization

• You are hired as an organizational consultant and asked to investigate why some work groups performed better than other work groups in a large organization

• In order to assess what's going on, you give each member of all the workgroups a survey to complete with questions about – how much they trusted one another– how often they went to one another for help.

Advice Vs. Trust

• Harris appointed head of strategic task force because of overall competence

• Problems in the task force arises because centrality in the advice network differs from centrality in trust network– Harris has high perceived competence go to him for advice– But few interpersonal skills– Benson central in trust network