This chapter introduces network theory, emphasizing its applications in social computing and its foundations in statistical physics and graph theory. It discusses key models like small world networks and the strength of weak ties, highlighting how relationships are represented through nodes and links. The chapter also covers the historical development of network theory, significant contributions by researchers, and the importance of understanding social networks for analyzing and optimizing communication and relationships.

1. Chapter 2 Network Theory
patterns within small groups, studies of
An 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 tell
you about the major researches that took Network Models
place since its conceptualization. Since the Networks are designed rigorously based on
course in question is social computing the their mathematical modeling. Some of the
chapter is written in a way to give examples most discussed network models are: Random
graphs, Small world networks, Scale-free
and illustrations which mostly relate to social
networks, etc.
computing. It also contains theories and
information which are mostly related to Network Theory
network theory and have some or no relation
“Network theory is an area of applied
to social computing. But the basic purpose of
mathematics, network science and a part of
this chapter is to explain Network theory and
graph theory. It is concerned with the study of
its applications in the field of social
graphs as a representation of either
computing.
symmetric relations or, more generally, of
asymmetric relations between discrete
What is a Network
objects”.
A network is a set of relationships comprised
of two objects, viz. vertices and nodes pair- REF: http://en.wikipedia.org/wiki/Network_theory
wise connected with each other. Network
systems are scattered around us such as: The concept of network theory came into
social networks, World Wide Web, Internet, being during the 1930’s.This was the work of
airport networks, etc. In networking an informal group of German psychologists
terminology, nodes are represented by
who specialized in “Gestalt Psychology”. At
people, items, computer servers, airports, and
the links are represented by friendships, that time it was considered more of a social
flights, physical connections. science tool. During 1950 this changed when
Cartwright and Harary connected network
theory with graph theory and other
Social Networks mathematical applications. After that two
“A social network is a social structure made threads were now researching network
up 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 other
more specific types of interdependency, , such thought of it as a structural science which lead
as friendship, kinship, common interest,
to the creation of different mathematical
financial exchange, dislike, sexual
relationships, or relationships of beliefs, models of network structure and other
knowledge or prestige”. (Ref: interesting phenomenon examples of which
http://en.wikipedia.org/wiki/Social_network) include small world phenomenon, strength of
weak ties etc.
Social science is one of many other disciplines
where quantitative study of real world Major Research in Network
networks has been carried out extensively. Theory
The topics that have been explored at length
The concept of network theory after it’s
in social networks research includes: early
recognition as a mathematical application
studies of Jacob Moreno (1920s) on friendship
grew at a steady pace. Although it has
4

2. Chapter 2 Network Theory
become more and more complex due to could now be described using quantitative
complex networks in the modern world still it graph theory descriptions. An example of this
has become very popular and grown its would be the social balance theory which
branches into diversified fields such as states that:
computer networks, biological ecosystems,
“Social balance theory is a class of theories
business management, particle physics,
computer science, economics, operations within social network theory which attempts
to describe how individual desires to reduce
research and other domains such as sociology.
But the major contributions in the Network affective cognitive dissonance influence in a
group of network structures, and that
theory field were made by a few scientists
which 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 World
study that the psychological state of an
individual within a group is affected by the
“In mathematics, physics and sociology a
relations within a group. The model depicted small-world network is a type of
the individuals as dots, which later came to be mathematical graph in which most nodes are
known as nodes and the relation between the not neighbors of one another, but most nodes
various members as lines or in more scientific can be reached from every other by a small
terms 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 1000
This 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, the
network analysis. This became known as a 1000 people you know each know 1000
tool for measuring and analyzing social unique others and they each know 1000
networks. others, and so on (Kadushin, 2004).
Cartwright and Harary Distance between any Two Nodes
1956 Cartwright a sociologist and Harary a The issue of distance between any two nodes
mathematician wrote a publication which was raised by Milgram (Milgram 1967) that
claimed that the sociograms like the one can be applied to all levels of network
analysis. The distance between two nodes is
Moreno 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 the
were describing social networks in qualitative network; (2) the extent to which nodes in the
terms, but with the contribution of Cartwright network have overlapping members in their
and Harary these qualitative descriptions first order zones; (3) barriers between nodes;
(4) agency exercised by the nodes.
4

3. Chapter 2 Network Theory
Strength of Weak Ties
In 1973, Mark Garnovetter (1973) published a
The Effective Distance between
very famous theory known as “Strength of
Nodes
weak Ties”. This theory was based upon the
This principle says that the impact of a zone small world theory and states that in cases of
on an individual node declines exponentially, job searching weak relations are more
when there can be an infinite number of effective than the strong ones. Meaning that
zones, in principle. That is, whatever is being family friends and relatives might not be as
studied, nodes have relatively small effects on much help in finding jobs as acquaintances
the focal individual or structure (Poulin et al., since these acquaintances belong to a
2000). completely different social group than yours.
The Size of the Interpersonal These were some of the theories which
Environment revolutionized the Network theory field and
According to this principal, the number of there are still more like the Watts and
people in an average size of 300 to 5000 Strongatz (1998) small world theory which
interpersonal individuals environment varies have left a mark in the history of Network
depends on how this environment is
theory.
measured and society in which focal person is
embodied (Bernard, Johnsen, Killworth, and
Robinson 1989). Let me tell you how and when you can use
network theory. Given an already existing
Six Degrees of Separation network, network theory can be used to
1960s Stanley Milgram experimented and analyze and optimize that given network and
confirmed the authenticity of very popular also understand the flow of information
still unproven hypothesis. The hypothesis throughout the network. Since we are
states that everyone in the world is connected studying network theory in order to
by six degrees of separation. This means that understand Social Computing we will be using
if 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 in
difference between any two nodes (taking the logistical problems and network load
shortest route possible) would not be more problems in business thus we will not be
than 6 nodes on average. This hypothesis was going into much depth about the optimization
tested by Milgram through an experiment in part of Network theory.
which he distributed letters throughout the
nation addressed to a single person along Weak Ties Help to Integrate social
with a letter which told the receiver to send Systems
the letter to either the person to whom the “The macroscopic side of this communication
letter was addressed to (given they knew him) argument is that social systems lacking in
or 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, scientific
its destination but those that did took an endeavours will be handicapped, and
average 6 people to find their way to the subgroups that are separated by race,
person. ethnicity, geography or other characteristics
4

4. Chapter 2 Network Theory
will 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 Sociology
In simple terms network optimization is the 781360-1380.
use of network theory mathematics to
identify the current network and find the Granovetter, Mark S. 1982. "The Strength of
optimum 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 transferring
goods from one place to another can be Kadushin, C., 2004. Introduction to Social
derived 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, draft
and effectiveness. version of chapter 2, accessed 23 May 2011
Milgram, Stanley. 1967. "The Small-World
Network 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, Group
articulated, spoken about, or conceptualized Psychotherapy and Sociodrama. New York:
by the participants in a network. Degree Beacon House
analysis technique helps analyze social
Pool, Ithiel d. S. and Manfred Kochen. 1978.
network’s strength and other Characteristics.
"Contacts and Influence." Social Networks
It should be remembered that the network
1(1):5-51.
does not end here. It is very essential to
understand 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 in
hope to relate the facets of social computing
Social Networks." Social Networks
with.
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-World'
Killworth, and Scott Robinson. 1989. Networks." Nature 393440-442.
"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
4