NetworkTheory

by Erlan Bakiev, Ph. D.

Zirve UniversitySpring 2012

Collaborative Network• The collaborative-network perspective is an emerging

alternative to resource- dependence theory. • Companies join together to become more competitive and to

share scarce resources. • Large aerospace firms partner with one another and with

smaller companies and suppliers to design next-generation jets. • Large pharmaceutical companies join with small biotechnology

firms to share resources and knowledge and spur innovation. • Consulting firms, investment companies, and accounting firms

may join in an alliance to meet customer demands for expanded services.

Why Collaboration?

• Some key reasons include sharing risks when entering new markets, mounting expensive new programs and reducing costs, and enhancing organizational profile in selected industries or technologies.

• Cooperation is a prerequisite for greater innovation, problem solving, and performance.

Case• Procter & Gamble (P&G) and Clorox are fierce rivals in

cleaning products and water purification, but both companies profited when they collaborated to produce Glad Press ’n Seal. The technology for the innovative plastic wrap was invented in P&G labs, but the company didn’t have a plastic-wrap category of products. Managers approached Clorox with the idea of a joint venture to market the new plastic wrap under the well-established Glad brand name. Glad’s share of the wrap market shot up 23 percent virtually overnight with the introduction of Glad Press ’n Seal

Definition of Social Networks

• “A social network is a set of actors that may have relationships with one another. Networks can have few or many actors (nodes), and one or more kinds of relations (edges) between pairs of actors.” (Hannemann, 2001)

History • 17th century: Spinoza developed first model

• 1937: J.L. Moreno introduced sociometry; he also invented the sociogram

• 1948: A. Bavelas founded the group networks laboratory at MIT; he also specified centrality

History Cont.• 1949: A. Rapaport developed a probability

based model of information flow

• 50s and 60s: Distinct research by individual researchers

• 70s: Field of social network analysis emerged.• New features in graph theory – more general

structural models• Better computer power – analysis of complex

relational data sets

Social Networks

• A social network is a social structure made up of a set of actors (such as individuals or organizations) and the dyadic ties between these actors (such as relationships, connections, or interactions).

• A social network perspective is employed to model the structure of a social group, how this structure influences other variables, or how structures change over time.

• The study of these structures uses methods in social network analysis to identify influential nodes, local and global structures, and network dynamics.

• Social networks are distinct from information, biological, or electrical networks, but theories and methods generalizing to all of these complex networks are studied in the field of network science.

Social Networks Cont.

• Social networks and the analysis of them is an inherently interdisciplinary academic field which emerged from social psychology, sociology, statistics, and graph theory.

• Scholars in these and other areas have used the idea of "social network" loosely for almost a century to connote complex sets of relationships between members of social units across all scales of analysis, from the local to the global as well as the scale-free

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Social Networks Cont.

• Jacob Moreno is credited with developing the first sociograms in the 1930s to study interpersonal relationships as structures in which people were points and the relationships between them were drawn as connecting lines.

Social Network Cont.

Social Network• The term is used to describe a social structure

determined by such interactions. • The ties (sometimes called edges, links, or

connections) in the structure are called "nodes”.• The nodes through which any given social unit

connects represent the convergence of the various social contacts of that unit.

• Many kinds of relationships may form the "network" between such nodes, but interpersonal "bridges" are a defining characteristic of social networks.

• Social network approaches are useful for modeling and explaining many social phenomena.

• An axiom of the social network approach to understanding social interaction is that social phenomena should be primarily conceived and investigated through the properties of relations between and within units, instead of the properties of these units themselves.

Social Network Cont.

• One common criticism of social network theory is that individual agency is essentially ignored.

• Although this is not the case in practice (see agent-based modeling). Precisely because many different types of relations, singular or in combination, form into a network configuration, network analytics are useful to a broad range of research enterprises.

Social Network Cont.

Representation of Social Networks• Matrices

• Graphs

Nick

Ann

Rob

Sue

Sources: http://www.andrew.cmu.edu/user/krack/krackplot/mitch-circle.html

http://www.andrew.cmu.edu/user/krack/krackplot/mitch-anneal.html

Visualization Software: Krackplot

Friend Network

• Oh, Susarla, and Tan 2007

Subscriber Network

• Oh, Susarla, and Tan 2007

OSS Collaboration Network

• Singh, Tan, and Mookerjee 2007

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• Zhang and Tan 2007

Connections (based on Hanneman, 2001)

• Size  • Number of nodes

• Density • Number of ties that are present the amount of

ties that could be present

• Out-degree • Sum of connections from an actor to others

• In-degree • Sum of connections to an actor

Distance (based on Hanneman, 2001) • Walk

• A sequence of actors and relations that begins and ends with actors

• Geodesic distance • The number of relations in the shortest possible

walk from one actor to another

• Maximum flow • The amount of different actors in the

neighborhood of a source that lead to pathways to a target

Some Measures of Power (based on Hanneman, 2001)

• Degree• Sum of connections from or to an actor

• Closeness centrality• Distance of one actor to all others in the

network

• Betweenness centrality• Number that represents how frequently an actor

is between other actors’ geodesic paths

Cliques and Social Roles (based on Hanneman, 2001)

• Cliques • Sub-set of actors

• More closely tied to each other than to actors who are not part of the sub-set

• Social roles • Defined by regularities in the patterns of

relations among actors

Examples of Applications (based on Freeman, 2000)

• Visualizing networks

• Studying differences of cultures and how they can be changed

• Intra- and interorganizational studies

• Spread of illness, especially HIV

Source: http://www.orgnet.com/sna.html

Commercial Application

Dynamic Networks (based on Carley, 2003)

• Limitations to traditional social network analysis• Focused on small bounded networks

• With 2-3 types of links among one type of nodes • At one point of time • Close to perfect information

Network Theory

• Network theory is an area of computer science and network science and part of graph theory.

• It has application in many disciplines including statistical physics, particle physics, computer science, biology, economics, operations research, and sociology.

Network Theory Cont.

• Network theory concerns itself with the study of graphs as a representation of either symmetric relations or, more generally, of asymmetric relations between discrete objects.

• Applications of network theory include logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc.

Social Network Analysis• Social network analysis examines the structure of

relationships between social entities. • These entities are often persons, but may also be

groups, organizations, nation states, web sites, scholarly publications.

• Since the 1970s, the empirical study of networks has played a central role in social science, and many of the mathematical and statistical tools used for studying networks have been first developed in sociology.

Social Network Analysis Cont.

• Amongst many other applications, social network analysis has been used to understand the diffusion of innovations, news and rumors.

• Similarly, it has been used to examine the spread of both diseases and health-related behaviors.

• It has also been applied to the study of markets, where it has been used to examine the role of trust in exchange relationships and of social mechanisms in setting prices.

Social Network Analysis

• Similarly, it has been used to study recruitment into political movements and social organizations.

• It has also been used to conceptualize scientific disagreements as well as academic prestige.

• More recently, network analysis (and its close cousin traffic analysis) has gained a significant use in military intelligence, for uncovering insurgent networks of both hierarchical and leaderless nature.