Creating Real Time Connections - Application of Scale Free and Random Networks - Research Paper Example

Abstract The concept of creating a social network has altered over time with various theories and applications that apply to the main networking system. When looking at scale – free and random networks, it can be seen that there are specific applications which now can be used. The networks now include an understanding of how technologies show the networking system working. This paper will examine and define these two theories of networking and communication. This will be furthered by an understanding of how the theories are limited. The experimentation will examine how this particular theory works as well as what can be applied and what the limitations are in creating effective social networks, specifically with the application of online methods that are used with current social networking techniques. Keywords: scale – free networks, random networks, online networks, power law, Introduction The representation of a network is one which is defined through several methodologies and theories, all which are able to create an understanding of how social patterns work. Theories which may be applied to the development of networks and social interaction include scale – free networks and random networks. Both of these specific types of models identify the way in which social interactions occur as well as the effectiveness of specific types of networks. Today, scale free and random network theories are one of the most popular concepts, specifically when looking at the Internet and other newer pieces of technology that invite different formations and patterns with interactions. Identifying the degree of effectiveness of these two theories and understanding if they work in real world networks is one of the questions that arises when identifying these specific theories. This paper will examine the effectiveness of these two theories as well as the practical applications which apply to the concept of building networks. Statement Problem The concept of scale – free and random networks are known to work through a mathematical equation in which a degree distribution follows a power of law. A fraction of nodes are within a network and distribute to other nodes, all which are defined by a specific amount of distribution which occurs, usually within a given range of association to another individual. In scale – free networks, there are specific degrees in which the network interactions occur, while random networks are identified by the networks not carrying a degree distribution (Albert, Barabasi, 47: 2002). Theoretically, this particular theory shows how a distribution of networks can grow over a period of time and provide interactions with others in relation to others. However, real world networks may not apply this law with the social patterns that are followed. While the theory may have relevance mathematically, the different social laws and associations with real world networks alter the way in which these systems may work. The examination of how much these specific networks can work in a given situation as well as what the outcomes are when looking at real world networks in relation to this theory then creates a question of whether the concept of open networks are effective both in relation to theory and concepts of developing consistent networks. Defining Scale – Free Networks The concept of scale – free networks is one which has recently been established by theorists, such as Barbasi. The particular concept was generated after examination of complex systems, including natural settings and societal implications. Observations included the World Wide Web, human contacts and chemical networks of a cell. This particular theory states that there is a specific set of nodes that appear randomly next to each other or to a certain degree from each other. As these are developed, there is a determination of how the networks will connect to the other by distributions from one connection to the next. The degree distribution is determined by the randomness of where the nodes are placed as well as how closely the distribution can move through the degrees which are created from the nodes and the connections made (Barabasi et al, 559: 2001). The concept of the scale – free networks are inclusive of growth and attachment that occurs between different correlations. Individuals work as the nodes in the instance of networking, in which each automatically attracts to the next node, despite the distance. The power of distribution then becomes important in creating a specific connection and development of networking. The correlations between individuals can expand outward and also can decrease or be removed. When this occurs, the node, or individual, will associate with the next connection, or node, which is in the network. Ultimately, this leads to each individual connecting not only to the next, but also allows the individual to be connected to others that are more degrees apart than the initial connections (Santos, Pacheco, 1649: 2005). This specific theory can be seen in image 1. Image 1: Scale – Free Network Theory This particular image shows how there is a direct connection to the nodes which appear closest to the surrounding nodes. However, there is also an indirect connection that moves by specific degrees to nodes that are placed in more external networks, essentially which leads to a connection to the initial nodes. For the particular concept of nodes to connect to work effectively, a power law distribution is applied. The power law has the exponent “y”, which is the in between of the nodes. The power law states that the node will move from one distance to the next with the shortest distance of “y” being the connection which is made. Each node then works as a data packet which carries information between nodes. When the vertices can move a shorter distance to the next node, it provides more power in the connection, interaction and overall network. With the power law, the range carries the equation of 2 Read More