Network analysis is a research approach that is suited to describing, exploring, and understanding various types of structural and relational aspects. Important contributions were made from an extremely wide variety of fields, including sociology, psychology, political science, anthropology, communication, business, mathematics, statistics, computer science, and physics.
Typically, a network consists of actors that represent individuals, organizations, programs, or other entities. Further, a network can be four different things: a conceptual model, a description of an existing real-world structure or system, a mathematical model, or a simulation. In its background and broad sense, network analysis is a field that mostly concerns itself with relational data and research questions. More specifically, the network paradigm has four important features:
A history of network analysis approaches can be traced back to the Eighteenth century. In that century, European mathematician Leonhard Euler used a visual representation of a network of bridges and rivers to solve the now famous Königsberg bridge problem. The problem asked if it was possible to walk around the town of Königsberg, crossing each of its seven bridges only once, and returning to the point of origin. By portraying the bridges and land as points with lines between them, Euler determined that no such path existed owing to the number of nodes and links. In doing so, Euler invented graph theory, which provides one of the mathematical foundations for network analysis. Later, throughout the 1800s and early 1900s social scientists posed questions about social relations and developed theories and terminology to describe social connections and social structure.
In 1929 a new idea about ties between people was proposed in a short story by Hungarian writer Frigyes Karinthy. In the story, a character asserted that he could link anyone in the world to himself through at most five acquaintances, proposing what may be the first mention of the concept of six degrees of separation. In the 1920s educational psychologists published a number of studies reporting on characteristics of social ties such as influence, interaction, and companionship.
Major contributions to the method were made in 1934 by psychiatrist Jacob L. Moreno. Moreno developed a new way of representing relationships on paper, called a sociogram. A sociogram was a drawing with points representing people connected by lines representing interpersonal relationships. Morenos work established network analysis as a unique discipline, and his sociograms were the first specific network analytic tool.
In 1959, mathematicians Paul Erdõs and Alfréd Rényi, found out with their model that the larger the size of the network, the fewer connections between network nodes were needed to have the network be completely linked.
In the early 1970s sociologist Mark Granovetter posited that, in addition to strong ties to families and neighbors, each person has certain weak ties to casual acquaintances and that these weak ties hold a network together. Herein, the acquaintances and friends of friends could reach outside what might otherwise be closed and therefore allowed a larger network to form.
Granovetters work was important for several reasons; it helped the development of a sophisticated and realistic model of network structure. Furthermore, Granovetters work was among the first applications of network theory, which attempted to explain social structure and human behavior. Granovetters findings led to a deeper understanding of how knowledge and information can be efficiently passed through large social networks.
"The information revolution has given birth to new economies structured around flows of data, information, and knowledge. In parallel, social networks have grown stronger as forms of organization of human activity." 
One of the obvious advantages in doing network analysis is that very complex and incomprehensible amounts of connections can be made clear and structured. This way conclusions can be drawn about a large quantity of connections that otherwise would seem irrelevant or too complicated. In the political case example, the use of certain words can be linked to the voting behavior of respectively democrat or republican voters. Without the use of network analysis this specific kind of research into voting behavior would be almost impossible.
Another advantage of network analysis can be seen in the work of Florence Nightingale: by analyzing all the different causes of mortality and connecting them in a comprehensive network, the military could take adequate measures to prevent a significant number of deaths. This example shows that by using network analysis, you can literally save lives.
In the digital age the advantages of network analysis are being used more and more. If it is by connection with all your real life affiliates online in networks as Facebook, Twitter or Google+, or by using your network to find a job or search for the right employee on LinkedIn; the ways in which you can expand and use your network by analyzing the different connections are huge. Because of all the criteria that can be analyzed the possibilities for doing an exact search can be specified very precisely within the set boundaries. This way the connections between all kinds of people are getting tighter, while the different characteristics of these people can simultaneously be specified and examined.
One of the disadvantages of using network analysis is that people might have the tendency to solely focus on the big picture, thus neglecting all the small and sometimes personal/human factors that also play a role in a certain analysis. For example in the Florence Nightingale case, all the cases of mortality are being compiled in a massive death database where every single number represents the death of a human being. By looking at the loss of life in such a calculating way might invoke a certain utilitarian viewpoint that is considered immoral or unethical by some.
One of the more dividing disadvantages of network analysis is that researchers only look at networks for reaching their conclusions; thereby overlooking a rather significant number of people that do not participate in those kind of networks. A very relevant example can be shown with online network analysis: because before people can get online they must have access to a number of (digital) resources that require a certain set of funds and skills. Some people simply dont have these and consequently can not be a part of these networks, or the resulting analysis.
Those who are most deprived socially are also least likely to have access to digital resources such as online services." 
So the people that are already on the fringes of (online) society are getting more and more polarised because of the disadvantages they have for getting acces to certain networks. And when the instruments that the majority of researchers use include a lot of network analysis, these people wont get included in the result. So they wont get the benefits that can be accomplished by doing these kind of studies.
This study has shown that digital disengagement is persistent and related to social disadvantage. The implications of these findings indicate that digital disengagement is not simply an academic issue of little relevance to social policy technology and social disadvantages are inextricably linked. This means that social policy goals will be increasingly difficult to realise as mainstream society continues to embrace the changes in our information society while those on the margins are left further behind disengaged digitally, economically, and socially.
Visualization as research method:
Presentation of data, communication of data. It is strong to the notion of exploration and all about learning something about the data. Underlining the visualization tools as ways to get to research. It becomes an interactive process, by trying to find out things in the data.
There have been several studies using visualizations to explore relations, in networks. Social network visualizations have always been popular. In these visualizations the relations with people to x fulfill a central role. Through the years there have been many different kinds of x-es. The social has been brought into relation with politics, diseases, war, economics, art and other social elements such as friendship connections.
One of the first used network graphs were used by Florence Nightingale. She was able to convince and change a lot through the usage of statistics and the visualization of a network. She was able to show the correlation between the organization of the military (or lack off) and the mortality rate. She used visualization to demonstrate the hidden killer in the army, and vastly decrease the mortality rate.
(The figure below shows the total mortality rate, the darkest outer one are the numbers that could have been prevented).
In the American elections, network visualization has been used to link certain words and ideas. Republican or democratic sides were linked to words by counting the number of mentioning. This visual helps to see connections between thoughts and sides, a representation of topics?
Friends and social:
An interactive graphic displaying the number of friends and showing possible (historical) relations to specific countries.
Relations in the Bible:
"The most direct way to study social structure is to analyze the patterns of ties linking its members. Network analysts search for deep structures - regular network patterns beneath the often-complex surface of social systems."Moreno would later add another innovation, namely the sociogram, to his Vitea. That would be a systematic method for graphically depicting the interpersonal structures of groups representing individuals as points and relationships as lines linking between them (Wasserman and Faust 1994). His approach would eventually lead to modern social network analysis. Sociologist Barry Wellman is another prolific scholar in the field of social network analysis. Wellman is quite famous for his international organization that strings Social Network Analysis researchers together. INSNA, a acronym for International Network Society of Social Network Analaysts, is still very influential in the field of social network analysis.. And so is Wellman. Wellman published many research on network analysis (more than 300 articles, chapters, reports and books). He thought of countless new concepts, such as networks of networks and personal community. INSNA website: http://www.insna.org/index.html
"Harvard's sociology department became a centre of social network analysis under the leadership op Harrison White. This time period at Harvard has been highlighted by many as the critical moment in network analysis."Under the supervision of professor Harrison White, many Harvard students have published in social network analysis. Barry Wellman was one of them. White wrote a book in which he demonstrated the use of mathematics in sociology, but he is mostly praised for his research with students. More specific: his work on roles and positions. Boorman, White. Social Structure from Multiple Networks http://www.jstor.org/discover/10.2307/2777596?uid=3738736&uid=2129&uid=2&uid=70&uid=4&sid=21102667490207
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