Barabasi-Alberts Scale-Free Network and Watts-Strogatz Small-World Network - Case Study Example

This paper thereby digs deeper into two most commonly used network models: (i) Barabasi-Albert’s scale-free network, and (ii) Watts-Stogatz’ small-world network. The Barabasi-Albert network model refers to the algorithm for generating random scale-free networks through the use of preferential attachment mechanisms. The model delineates the formation of networks, which result in the small-world phenomena- an idea that an individual is just a couple of connections away from any other person in the real world. Through these two theories, the paper further uses the two network models to explain various phenomena in real-life situations, such as the spread of viral diseases, internet or computer viruses, and human relationships among other interconnected networks.

Barabasi-Albert’s Scale-Free Network and Watts-Strogatz Small-World Network
1. Introduction
In the contemporary world, the widespread prevalence of networked systems, technical applications, as well as the business world’s networks has made many changes within the field of information systems. As a result, a number of researches on these networks have been in place, aiming at analyzing the topology of such networks as well as processes that are involved in them. Several models have been formed and used over decades to explain the dynamics in the world’s systems of networks, especially in the fields of technology, social, economic, and information systems. This paper, however, narrows down to two commonly used network models: Barabasi-Albert’s scale-free network, and Watts-Strogatz's small-world network. The Barabasi-Albert model denotes the algorithm for the generation of random scale-free networks through the use of preferential attachment mechanisms. Here, the scale-free networks are widely viewed via natural and human-made systems, such as the internet, citation networks, World Wide Web, as well as social networks. On the other hand, the Watts-Stogatz’ small-world model is a model for generating random graphs with small-world scenarios or properties such as high clustering, and short average path lengths. The model delineates the formation of networks, which result in the small-world phenomena- an idea that an individual is just a couple of connections away from any other person in the real world.

2. Barabasi-Albert’s Scale-Free Network
A free-scale network is a network with a degree of distribution that follows the law of power asymptotically. A number of observed networks fall within the class of scale-free networks- having a power-law degree of distributions. This model incorporates two vital general concepts of growth and preferential attachment. Both preferential attachment and growth widely exist within the real networks. Growth refers to the increment of the number of nodes over time, while the preferential attachment denotes the theory that the more connected a node is, the higher the likeliness that it receives new links. Higher degree nodes have a strong ability to grab additional links to the network. On the other hand, preferential attachments can innately be implicit when one's notion is in terms of people’s connection through social networks.