The Power Law

The power law refers to polynomial relationships where scale invariance is evident. It involves the projected relationship between the magnitude of a physical stimulus and its perceived intensity. The power law is evident in social structures. In order to understand power laws in social structures, it is vital to determine the virtual location of a person within a social network by analysing its connections and relationships with surrounding entities. The two social network measures for this kind of analysis are known as ‘betweeness’ and ‘closeness’. It predominantly discloses the nodes beneficial or constrained location in a particular network. Both these measures are dependent upon the nodes existence within the fixed connection patterns involved in the network.

Betweeness is the measurement of a node’s control over what flows in the network, and closeness refers to the measurement of a node’s accessibility to available information via a network. When a node adopts higher levels of control and accessibility through its connections, they begin to gain the power to control other nodes within the network. There are networks with centralised power such as hierarchy and hub-and-spoke structures. This often consists of a collection of nodes with a vast amount of connections, and others with fewer connections. These types of network structures demonstrate the notion of unequal distribution of power. It is important to note that the distribution of power increases as the disconnection nodes begin to interact and connect with the other nodes in the network. This reflects the idea that diversity and freedom of choice tends to generate inequality; therefore the greater the diversity, the greater the extremity of inequality.

There are networks where individuals have the freedom to choose between various options. These types of systems promote uneven power law distributions where a small portion of the system experience an inequitable amount of traffic compared to other individuals involved in the system. This is not a reflection of moral weakness, selling out, or any other psychological explanation. Power law distribution is a result of the very act of freedom and choice. Freedom of choice has the potential to create unequal distributions. Because the curve is so heavily weighted towards the top performers, most elements in a power law system are below average (refer to diagram A for an illustration of a ‘Power Law Curve’). Despite the size of any network, freedom and diversity has the potential to create power law distributions.

Diagram A – Power Law Curve

Through Alberto-Laszlo Barabasi, Duncan Watts and Bernardo Huberband network theories, we recognise that power law distributions are inclined to take place in social systems where people have the freedom to express their preferences amongst a set of options. The theory proposes that the more preferential attachments and connections a node obtains, the higher their connectivity rate will become. The initial connectivity difference between two nodes may further increase as a network expands in size, therefore the longer the node exists in a network the higher their connectivity rate will be in comparison to the younger nodes of the network. This concept reflects a ‘rich-get-rich’ or the ‘winner-takes-all’ phenomenon. Vilfredo Pareto is an Economist that made the observations that wealth follows a “predictable imbalance”, with 20 percent of the population holding 80 percent of the wealth. In the last century, investigators have discovered power law distributions in human systems.


References:

Department of Physics, University of Notre Dame (2000).
Power-Law Distribution of the World Wide Web. SCIENCE (vol. 287)

Valdis Krebs (2004), Power in Networks
From http://www.orgnet.com

Clay Shirky (2003), Power Laws, Weblogs and Inequality,
From http://www.shirky.com/writings/powerlaw_weblog.html

The Small World Theory

The small world theory studies the average path lengths in social networks. The concept of the average path length in network topology involves calculating the number of steps along the shortest path between every possible pair of nodes in a network. This measurement involves the study of network theory where the information transfers and connection between nodes are examined. Any two individuals in a social network are likely to be connected though a short sequence of intermediate acquaintances. Short average path lengths are most desirable in networks.



In the 1960’s a social psychologist by the name of Stanley Milgram conducted the “small-world experiment”. His experiment suggests that the human society can be referred to as a ‘small world’ due to the short path lengths connecting any two individuals in the world. He conducted this experiment by tracing chain letters and investigating the short chains of acquaintances that connected a pair of strangers in the United States. Milgram discovered that a successful chain letter required five to six intermediary steps before reaching the desired destination. Today, Milgram’s principle is commonly referred to as “six degrees of separation”. This is a fundamental principle in social networks and emphasises the short paths that link any two people in the world who know one another.

Recent work has proposed that the small world phenomenon is omnipresent in networks that involve nature, technology and the underlying element in the structural advancement of the World Wide Web. The “Small World Research Project” investigates Milgram’s theory and additionally conducts research on the types of barriers that seem to divide the society; whether it concerns an individual’s characteristic such as age, race or level of education. Information, news and opinions continuously spread through the world wide social structure. The way a single piece of information spreads on a global scale has always been a mystery. This small world theory is ever more fascinating in the digital age.

References:
David Liben-Nowell and Jon Kleinberg (2008).
Tracing information flow on a global scale using Internet chain-letter data. (vol. 105, no.12)

Judith S. Kleinfeld (2002), Could it be a big world?.
From http://www.judithkleinfeld.com/ar_bigworld.html

Social Network Analysis

Social network analysis is the study of how relationships between entities in a social structure influence behaviour and beliefs. It is evident that causal pressures are present in social structures. Social network analysis examines the entities of a network and the importance of their relationships within other entities they interact with. Analysing a social network involves mapping and measuring the magnitude of relationships and flows between nodes such as people, groups, organizations, computers, web sites, and other information or knowledge processing entities. It incorporates theories, models and applications that are expressed in terms of related processes and concepts, and are reliant on the accessibility of relational data, rather than attribute data. Social network analysis provides both a visual and a mathematical analysis of human relationships. Networks can be illustrated in the following forms:

Dyads: two actors/nodes and their ties

Triads: three actors/nodes and their ties




Larger systems: subgroups of individuals or entire networks.

Network analysis techniques have the aptitude to analyse and distinguish structural features in a network; such as the structure of communication in an organisation. It is vital to investigate the relationship properties between and within entities involved in a network, rather than the properties of the individual entities. Generally, network analysis is the focus of relationships between people rather than their individual characteristics. Such relationships may encompass emotions individuals share, the exchange of information, or possibly the exchange of tangible goods. When mapping out the relationships in a social network, we can gain a clearer understanding of the communication patterns involved in an organisation; whether it is an informal or a formal structure. The understanding of emerging patterns is beneficial in comprehending other organisational phenomena.

There are two basic types of network analysis that reflect two types of data: ego network analysis and complete network analysis. Ego network analysis can be undertaken through the exercise of traditional surveys. It typically involves assessing the quality of a network such as the size, diversity, average and income. Complete network analysis is the attempt of obtaining every relationship involved in the network; such as friendships between employees of a company. This is a vital technique in analysing subgroups and equivalence measures like centrality.

Social network analysis involves the study of an entity; its connection and relationship with the rest of the network.


References:

Ronald L. Breiger. (2004). The Analysis of Social Networks, Handbook of Data Analysis, pp.505-526, London: SAGE Publications

Universiteit Twente (2004), Network Theory and Analysis.
From http://www.cw.utwente.nl/theorieenoverzicht/Theory%20clusters/Communication%20and%20Information%20Technology/Network%20Theory%20and%20analysis_also_within_organizations.doc/_printableversion.html

Valdis Krebs (2008) , Social Network Analysis, A brief Introduction.
from http://www.orgnet.com/sna.html

Ulrike Gretzel (2001) , Social Network Analysis: Introduction and Resources
from http://lrs.ed.uiuc.edu/tse-portal/analysis/social-network-analysis/

Social Network Theory

Social network theory is a branch of social science that is non reductionist and applies to a variety of human organizations; from minor communities to major groups including the entire world population. The social relationships of these organisations are examined and described in terms of nodes and ties. Nodes denote the individual actors of a network, and ties allude to the relationship or link between the actors. A social network map or diagram illustrates the concept where nodes are often represented by points and ties are represented by lines. In the case of social networks, the objects refer to individuals or groups of individuals. For example, a network may involve an individual and the mapping of their connections with every other person they may be associated with; these mapping can be directional or bi-directional. The simplest network involves two nodes and their relationship; this is called a ‘dyad’. Subsequently, a network with three nodes is known as a ‘triad’. There are also larger networks that involve subgroups of individuals. Social network maps assist in the evaluation of ties, nodes and the social capitals of individuals.

The essence of social network theory defers from the traditional studies of sociology. Sociology studies works off the basis that an actor’s attributes are significant; however, social network theory presumes that the attributes of an actor are of less importance to their relationship and ties with other actors of the network. Social network theory is useful for describing many real-world phenomenas and proves that network structure influences the ability of individual agencies.

Social capital refers to the positioning of an individual in a network and its ability to obtain resources from other people who are involved in the same network. An individual with a higher number of connections will fundamentally acquire greater knowledge, influence and power. Social capital can have a substantial influence on a person’s life; affecting such aspects as job searches and potential for promotions.

Social networks have been advantageous in examining interactions between companies through the characteristics of links and associations shared between executives, employees and other allied affiliates. The essence of social networks provides companies with dynamic methods for collecting information, deter competition and even assist in the planning of price and policy settlements. It can also be useful when identifying groups and cliques.

The study of social networks is important since it helps us better understand how and why we interact with one another, as well as how technology can alter this interaction. The advancement of technology has introduced new areas of research. The field of social network theory has grown considerably during the past few years.


References:

Appalachian State University and York University (September 9, 2005),
Theories used in IS Research: Social Network Theory.
from http://www.istheory.yorku.ca/socialnetworktheory.htm

Charles Kadushin (February 17, 2004 ),
Introduction to Social Network Theory.
from http://home.earthlink.net/~ckadushin/Texts/Basic%20Network%20Concepts.pdf

Jason Ethier, Current Research in Social Network Theory.
from http://www.ccs.neu.edu/home/perrolle/archive/Ethier-SocialNetworks.html

Social Networking

Social networking is phenomena defined by the linking and building of relationships between individuals and specific groups that typically share a commonality. It refers to the structure of society that is simply a cluster of individuals who are interconnected on a variety of levels for a mutual benefit. Some examples include communities that involve individuals who share common hobbies, religion or political values.

Individuals have always social networked, but the Internet has introduced a whole new concept of networking in a global sense. The notion of online and offline social networking are similar. Online social networking involves the utilisation of social networking websites where individuals from around the globe have the facility to interact with one another. Just like offline social networking, individuals have the opportunity to interact with other people in a familiar environment where they can converse, participate in events, create private networks of their own and interact with existing public networks. The benefits of online social networking have become popular because society now have the ability to communicate through a range of mediums via the internet; such as emailing, instant messaging, file sharing, video conferencing and blogging. We can now build relationships with individuals and groups situated in different regions of the world without the need of travelling the physical distance.

The proliferation of popular social networking websites such as MySpace, Facebook, Bebo, YouTube and Friendster has been deliberately designed to provide a platform for the online population to interact with one another. The development of these platforms permits individuals to form private networks and interact with other public networks online. Several social networking websites have been intentionally designed to cater for the needs of a specific market.

LinkedIn focuses on professional networks which lists information such as previous employment and references. It has the ability to help individuals and businesses network, expand and keep record of their current contacts. These websites have the facility to assist people in maintaining their networks via a login rather than using the traditional paper address book and business card collection.

MySpace is a social networking website that tends to lure the younger demographics. This website is based on an ego-centric model where users have the ability to customise the appearance of their webpage to represent their persona. MySpace has become a social networking platform for musicians and performing artists to upload their music. Many independent bands have taken advantage of this functionality to promote themselves.

Facebook combines and enhances a collection of elements that exists in LinkedIn and MySpace. Facebook adopts a function that only allows authorised ‘friends’ to view a person’s profile page. It also permits users to search and contact strangers from different regions of the world. The ego-centric element is enhanced to allow self expression through news feeds about individuals and their personal activities.

Statistics reveal that the social demographics of Generation Y and Generation X seem to be the predominant users of social networking websites.


References:
http://www.whatissocialnetworking.com/
Fatpublisher (November 13, 2007), Social Networking Online,
from http://www.fatpublisher.com.au/resources.php?topic=6&article=14&page=1