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Chapter 2 Network Theory

An IntroductionThis chapter will introduce you to the field of science known as Network Theory and tell you about the major researches that took place since its conceptualization. Since the course in question is social computing the chapter is written in a way to give examples and illustrations which mostly relate to social computing. It also contains theories and information which are mostly related to network theory and have some or no relation to social computing. But the basic purpose of this chapter is to explain Network theory and its applications in the field of social computing.

What is a NetworkA network is a set of relationships comprised of two objects, viz. vertices and nodes pair-wise connected with each other. Network systems are scattered around us such as: social networks, World Wide Web, Internet, airport networks, etc. In networking terminology, nodes are represented by people, items, computer servers, airports, and the links are represented by friendships, flights, physical connections.

Social Networks“A social network is a social structure made up of individuals (or organizations) called "nodes", which are tied (connected) by one or more specific types of interdependency, , such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige”. (Ref: http://en.wikipedia.org/wiki/Social_network)

Social science is one of many other disciplines where quantitative study of real world networks has been carried out extensively. The topics that have been explored at length in social networks research includes: early studies of Jacob Moreno (1920s) on friendship

patterns within small groups, studies of business communities and sexual patterns, statistical physics community, etc.

Network ModelsNetworks are designed rigorously based on their mathematical modeling. Some of the most discussed network models are: Random graphs, Small world networks, Scale-free networks, etc.

Network Theory“Network theory is an area of applied mathematics, network science and a part of graph theory. It is concerned with the study of graphs as a representation of either symmetric relations or, more generally, of asymmetric relations between discrete objects”.

REF: http://en.wikipedia.org/wiki/Network_theory

The concept of network theory came into being during the 1930’s.This was the work of an informal group of German psychologists who specialized in “Gestalt Psychology”. At that time it was considered more of a social science tool. During 1950 this changed when Cartwright and Harary connected network theory with graph theory and other mathematical applications. After that two threads were now researching network theory. One thought of it as a study of social groups and their relations and the other thought of it as a structural science which lead to the creation of different mathematical models of network structure and other interesting phenomenon examples of which include small world phenomenon, strength of weak ties etc.

Major Research in Network TheoryThe concept of network theory after it’s recognition as a mathematical application grew at a steady pace. Although it has

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Chapter 2 Network Theory

become more and more complex due to complex networks in the modern world still it has become very popular and grown its branches into diversified fields such as computer networks, biological ecosystems, business management, particle physics, computer science, economics, operations research and other domains such as sociology. But the major contributions in the Network theory field were made by a few scientists which are as followed:

Moreno’s SociogramsIn 1937 one of the German psychologists “Moreno” created a model based on the study that the psychological state of an individual within a group is affected by the relations within a group. The model depicted the individuals as dots, which later came to be known as nodes and the relation between the various members as lines or in more scientific terms links. Example

This model gave rise to one of the most widely researched fields known as social network analysis. This became known as a tool for measuring and analyzing social networks.

Cartwright and Harary1956 Cartwright a sociologist and Harary a mathematician wrote a publication which claimed that the sociograms like the one Moreno built could be analyzed using graph theory (Davis, 1970). Till now the sociologists were describing social networks in qualitative terms, but with the contribution of Cartwright and Harary these qualitative descriptions

could now be described using quantitative graph theory descriptions. An example of this would be the social balance theory which states that:

“Social balance theory is a class of theories within social network theory which attempts to describe how individual desires to reduce affective cognitive dissonance influence in a group of network structures, and that individual expect to be exposed to balanced social situations. Social balance theory is a tool to

observe a social group evolving to a balanced” (Cartwright and Harary, 1956)

The Small World

“In mathematics, physics and sociology a small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps. (Ref: http://en.wikipedia.org/wiki/Small-world_network)

If the personal networks of people don’t overlap, then s/he can reach to entire world in two or three steps. Suppose a person in Pakistan know 1000 unique people that his siblings don’t know, then, each of those 1000 people may know 100 other unique people, and so on (Pool and Kochen 1978). Then, the 1000 people you know each know 1000 unique others and they each know 1000 others, and so on (Kadushin, 2004).

Distance between any Two NodesThe issue of distance between any two nodes was raised by Milgram (Milgram 1967) that can be applied to all levels of network analysis. The distance between two nodes is determined by following four parameters: (1) the size of the first order zone of nodes in the network; (2) the extent to which nodes in the network have overlapping members in their first order zones; (3) barriers between nodes; (4) agency exercised by the nodes.

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Chapter 2 Network Theory

The Effective Distance between NodesThis principle says that the impact of a zone on an individual node declines exponentially, when there can be an infinite number of zones, in principle. That is, whatever is being studied, nodes have relatively small effects on the focal individual or structure (Poulin et al., 2000).

The Size of the Interpersonal EnvironmentAccording to this principal, the number of people in an average size of 300 to 5000 interpersonal individuals environment varies depends on how this environment is measured and society in which focal person is embodied (Bernard, Johnsen, Killworth, and Robinson 1989).

Six Degrees of Separation1960s Stanley Milgram experimented and confirmed the authenticity of very popular still unproven hypothesis. The hypothesis states that everyone in the world is connected by six degrees of separation. This means that if a sociogram of the relations between the people of the world could be made then the difference between any two nodes (taking the shortest route possible) would not be more than 6 nodes on average. This hypothesis was tested by Milgram through an experiment in which he distributed letters throughout the nation addressed to a single person along with a letter which told the receiver to send the letter to either the person to whom the letter was addressed to (given they knew him) or just send it to someone they thought would know him. Not all the letters reached its destination but those that did took an average 6 people to find their way to the person.

Strength of Weak TiesIn 1973, Mark Garnovetter (1973) published a very famous theory known as “Strength of weak Ties”. This theory was based upon the small world theory and states that in cases of job searching weak relations are more effective than the strong ones. Meaning that family friends and relatives might not be as much help in finding jobs as acquaintances since these acquaintances belong to a completely different social group than yours.

These were some of the theories which revolutionized the Network theory field and there are still more like the Watts and Strongatz (1998) small world theory which have left a mark in the history of Network theory.

Let me tell you how and when you can use network theory. Given an already existing network, network theory can be used to analyze and optimize that given network and also understand the flow of information throughout the network. Since we are studying network theory in order to understand Social Computing we will be using examples of social network for analysis. Whereas optimization is mostly used in logistical problems and network load problems in business thus we will not be going into much depth about the optimization part of Network theory.

Weak Ties Help to Integrate social Systems“The macroscopic side of this communication argument is that social systems lacking in weak ties will be fragmented and incoherent. New ideas will spread slowly, scientific endeavours will be handicapped, and subgroups that are separated by race, ethnicity, geography or other characteristics

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Chapter 2 Network Theory

will have difficulty reaching a modus Vivendi” (Garnovetter 1982, p. 106).

Network OptimizationIn simple terms network optimization is the use of network theory mathematics to identify the current network and find the optimum path for optimizing the working within the network. For example in a given network for transportation given some constraints, the optimum path for transferring goods from one place to another can be derived using the network optimization techniques, thus lowering cost. Likewise other network can be optimized for high efficiency and effectiveness.

Network AnalysisIn network analysis there is a similar finding that relationships are not necessarily articulated, spoken about, or conceptualized by the participants in a network. Degree analysis technique helps analyze social network’s strength and other Characteristics. It should be remembered that the network does not end here. It is very essential to understand what a network is and based on the findings presented in the chapter, one can hope to relate the facets of social computing with.

ReferencesBernard, H. R., Eugene C. Johnsen, Peter D. Killworth, and Scott Robinson. 1989. "Estimating the Size of an Average Personal Network and of an Event Subpopulation." Pp. 159-75 in The Small World, ed. Manfred Kochen. Norwood, NJ: Ablex Publishing Co.

Cartwright, D., and Harary, F. 1956). Structural balance: A generalization of Heider’s theory. Psychological Review. 63, 277-292.

Davis, J.A. (1970). Clustering and hierarchy in interpersonal relations: Testing two

theoretical models on 742 sociograms. American Sociological Review. 35, 843-852.

Granovetter, Mark S. 1973. "The Strength of Weak Ties." American Journal of Sociology 781360-1380.

Granovetter, Mark S. 1982. "The Strength of Weak Ties: a Network Theory Revisited." Pp. 105-30 in Social Structure and Network Analysis, eds. Peter Marsden and Nan Linn. Beverly Hills, Ca: Sage.

Kadushin, C., 2004. Introduction to Social Network Theory. Available at: http://home.earthlink.net/~ckadushin/Texts/Basic%20Network%20Concepts.pdf, draft version of chapter 2, accessed 23 May 2011

Milgram, Stanley. 1967. "The Small-World Problem." Psychology Today 1(1):62-67.Moreno, Jacob L. 1953. Who Shall Survive? Foundations of Sociometry, Group Psychotherapy and Sociodrama. New York: Beacon House

Pool, Ithiel d. S. and Manfred Kochen. 1978. "Contacts and Influence." Social Networks 1(1):5-51.

Poulin, R., M.-C. Boily, and B. R. Mגsse. 2000. "Dynamical Systems to Define Centrality in Social Networks." Social Networks 22(3):187-220.

Watts, Duncan J. and Stephen H. Strogatz. 1998. "Collective Dynamics of 'Small-World' Networks." Nature 393440-442.