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# Network Theory

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This 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.

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### Network Theory

1. 1. Chapter 2 Network Theory patterns within small groups, studies ofAn Introduction business communities and sexual patterns,This chapter will introduce you to the field of statistical physics community, etc.science known as Network Theory and tellyou about the major researches that took Network Modelsplace since its conceptualization. Since the Networks are designed rigorously based oncourse in question is social computing the their mathematical modeling. Some of thechapter is written in a way to give examples most discussed network models are: Random graphs, Small world networks, Scale-freeand illustrations which mostly relate to social networks, etc.computing. It also contains theories andinformation which are mostly related to Network Theorynetwork theory and have some or no relation “Network theory is an area of appliedto social computing. But the basic purpose of mathematics, network science and a part ofthis chapter is to explain Network theory and graph theory. It is concerned with the study ofits applications in the field of social graphs as a representation of eithercomputing. symmetric relations or, more generally, of asymmetric relations between discreteWhat is a Network objects”.A network is a set of relationships comprisedof two objects, viz. vertices and nodes pair- REF: http://en.wikipedia.org/wiki/Network_theorywise connected with each other. Networksystems are scattered around us such as: The concept of network theory came intosocial networks, World Wide Web, Internet, being during the 1930’s.This was the work ofairport networks, etc. In networking an informal group of German psychologiststerminology, nodes are represented by who specialized in “Gestalt Psychology”. Atpeople, items, computer servers, airports, andthe links are represented by friendships, that time it was considered more of a socialflights, physical connections. science tool. During 1950 this changed when Cartwright and Harary connected network theory with graph theory and otherSocial Networks mathematical applications. After that two“A social network is a social structure made threads were now researching networkup of individuals (or organizations) called theory. One thought of it as a study of social"nodes", which are tied (connected) by one or groups and their relations and the othermore specific types of interdependency, , such thought of it as a structural science which leadas friendship, kinship, common interest, to the creation of different mathematicalfinancial exchange, dislike, sexualrelationships, or relationships of beliefs, models of network structure and otherknowledge or prestige”. (Ref: interesting phenomenon examples of whichhttp://en.wikipedia.org/wiki/Social_network) include small world phenomenon, strength of weak ties etc.Social science is one of many other disciplineswhere quantitative study of real world Major Research in Networknetworks has been carried out extensively. TheoryThe topics that have been explored at length The concept of network theory after it’sin social networks research includes: early recognition as a mathematical applicationstudies of Jacob Moreno (1920s) on friendship grew at a steady pace. Although it has 4
2. 2. Chapter 2 Network Theorybecome more and more complex due to could now be described using quantitativecomplex networks in the modern world still it graph theory descriptions. An example of thishas become very popular and grown its would be the social balance theory whichbranches into diversified fields such as states that:computer networks, biological ecosystems, “Social balance theory is a class of theoriesbusiness management, particle physics,computer science, economics, operations within social network theory which attempts to describe how individual desires to reduceresearch and other domains such as sociology.But the major contributions in the Network affective cognitive dissonance influence in a group of network structures, and thattheory field were made by a few scientistswhich are as followed: individual expect to be exposed to balanced social situations. Social balance theory is a tool to observe a social group evolving to a balanced”Moreno’s Sociograms (Cartwright and Harary, 1956)In 1937 one of the German psychologists“Moreno” created a model based on the The Small Worldstudy that the psychological state of anindividual within a group is affected by the “In mathematics, physics and sociology arelations within a group. The model depicted small-world network is a type ofthe individuals as dots, which later came to be mathematical graph in which most nodes areknown as nodes and the relation between the not neighbors of one another, but most nodesvarious members as lines or in more scientific can be reached from every other by a smallterms links. Example 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 1000This model gave rise to one of the most people may know 100 other unique people,widely researched fields known as social and so on (Pool and Kochen 1978). Then, thenetwork analysis. This became known as a 1000 people you know each know 1000tool for measuring and analyzing social unique others and they each know 1000networks. others, and so on (Kadushin, 2004).Cartwright and Harary Distance between any Two Nodes1956 Cartwright a sociologist and Harary a The issue of distance between any two nodesmathematician wrote a publication which was raised by Milgram (Milgram 1967) thatclaimed that the sociograms like the one can be applied to all levels of network analysis. The distance between two nodes isMoreno built could be analyzed using graph determined by following four parameters: (1)theory (Davis, 1970). Till now the sociologists the size of the first order zone of nodes in thewere describing social networks in qualitative network; (2) the extent to which nodes in theterms, but with the contribution of Cartwright network have overlapping members in theirand Harary these qualitative descriptions first order zones; (3) barriers between nodes; (4) agency exercised by the nodes. 4
3. 3. Chapter 2 Network Theory Strength of Weak Ties In 1973, Mark Garnovetter (1973) published aThe Effective Distance between very famous theory known as “Strength ofNodes weak Ties”. This theory was based upon theThis principle says that the impact of a zone small world theory and states that in cases ofon an individual node declines exponentially, job searching weak relations are morewhen there can be an infinite number of effective than the strong ones. Meaning thatzones, in principle. That is, whatever is being family friends and relatives might not be asstudied, nodes have relatively small effects on much help in finding jobs as acquaintancesthe focal individual or structure (Poulin et al., since these acquaintances belong to a2000). completely different social group than yours.The Size of the Interpersonal These were some of the theories whichEnvironment revolutionized the Network theory field andAccording to this principal, the number of there are still more like the Watts andpeople in an average size of 300 to 5000 Strongatz (1998) small world theory whichinterpersonal individuals environment varies have left a mark in the history of Networkdepends on how this environment is theory.measured and society in which focal person isembodied (Bernard, Johnsen, Killworth, andRobinson 1989). Let me tell you how and when you can use network theory. Given an already existingSix Degrees of Separation network, network theory can be used to1960s Stanley Milgram experimented and analyze and optimize that given network andconfirmed the authenticity of very popular also understand the flow of informationstill unproven hypothesis. The hypothesis throughout the network. Since we arestates that everyone in the world is connected studying network theory in order toby six degrees of separation. This means that understand Social Computing we will be usingif a sociogram of the relations between the examples of social network for analysis.people of the world could be made then the Whereas optimization is mostly used indifference between any two nodes (taking the logistical problems and network loadshortest route possible) would not be more problems in business thus we will not bethan 6 nodes on average. This hypothesis was going into much depth about the optimizationtested by Milgram through an experiment in part of Network theory.which he distributed letters throughout thenation addressed to a single person along Weak Ties Help to Integrate socialwith a letter which told the receiver to send Systemsthe letter to either the person to whom the “The macroscopic side of this communicationletter was addressed to (given they knew him) argument is that social systems lacking inor just send it to someone they thought weak ties will be fragmented and incoherent.would know him. Not all the letters reached New ideas will spread slowly, scientificits destination but those that did took an endeavours will be handicapped, andaverage 6 people to find their way to the subgroups that are separated by race,person. ethnicity, geography or other characteristics 4
4. 4. Chapter 2 Network Theorywill have difficulty reaching a modus Vivendi” theoretical models on 742 sociograms.(Garnovetter 1982, p. 106). American Sociological Review. 35, 843-852.Network Optimization Granovetter, Mark S. 1973. "The Strength of Weak Ties." American Journal of SociologyIn simple terms network optimization is the 781360-1380.use of network theory mathematics toidentify the current network and find the Granovetter, Mark S. 1982. "The Strength ofoptimum path for optimizing the working Weak Ties: a Network Theory Revisited." Pp.within the network. For example in a given 105-30 in Social Structure and Network Analysis, eds. Peter Marsden and Nan Linn.network for transportation given some Beverly Hills, Ca: Sage.constraints, the optimum path for transferringgoods from one place to another can be Kadushin, C., 2004. Introduction to Socialderived using the network optimization Network Theory. Available at:techniques, thus lowering cost. Likewise other http://home.earthlink.net/~ckadushin/Texts/network can be optimized for high efficiency Basic%20Network%20Concepts.pdf, draftand effectiveness. version of chapter 2, accessed 23 May 2011 Milgram, Stanley. 1967. "The Small-WorldNetwork Analysis Problem." Psychology Today 1(1):62-67.In network analysis there is a similar finding Moreno, Jacob L. 1953. Who Shall Survive?that relationships are not necessarily Foundations of Sociometry, Grouparticulated, spoken about, or conceptualized Psychotherapy and Sociodrama. New York:by the participants in a network. Degree Beacon Houseanalysis technique helps analyze social Pool, Ithiel d. S. and Manfred Kochen. 1978.network’s strength and other Characteristics. "Contacts and Influence." Social NetworksIt should be remembered that the network 1(1):5-51.does not end here. It is very essential tounderstand what a network is and based on Poulin, R., M.-C. Boily, and B. R. M ‫ג‬sse. 2000.the findings presented in the chapter, one can "Dynamical Systems to Define Centrality inhope to relate the facets of social computing Social Networks." Social Networkswith. 22(3):187-220.References Watts, Duncan J. and Stephen H. Strogatz.Bernard, H. R., Eugene C. Johnsen, Peter D. 1998. "Collective Dynamics of Small-WorldKillworth, and Scott Robinson. 1989. Networks." Nature 393440-442."Estimating the Size of an Average PersonalNetwork and of an Event Subpopulation." Pp.159-75 in The Small World, ed. ManfredKochen. Norwood, NJ: Ablex Publishing Co.Cartwright, D., and Harary, F. 1956). Structuralbalance: A generalization of Heider’s theory.Psychological Review. 63, 277-292.Davis, J.A. (1970). Clustering and hierarchy ininterpersonal relations: Testing two 4