Critically assess, compare and contrast the RANDOM NETWORK and the Essay

Critically assess, compare and contrast the RANDOM NETWORK and the SCALE-FREE network proposed by Barabasi and Albert. With the - Essay Example An examination of the vulnerability of scale-free networks is also discussed in this paper, and the effect of power law distribution on the network topology is analyzed. The removal of nodes in these network models and the effects of such removal are discussed. The contrast between Scale-free networks and random networks in the area of resisting failures is analyzed, as it has been suggested that the strongly connected nodes are responsible for the failure of scale-free networks. This paper also includes some theoretical syntheses, the proposal of new and exploratory conceptual models, theoretically grounded discussions of methodology, the analysis of historical developments with clear implications for current and future theory, theoretically relevant discussions of timely and important network issues, and comprehensive literature reviews with strong theoretical implications. INTRODUCTION In recent history, evolving networks have been seen as a relevant and very popular area of resea rch among physicists. Reka Albert and Albert-Laszlo Barabasi introduced a concept of evolving networks that is based on preferential attachment, in order to understand the areas from which the ubiquity of scale-free distributions in real networks originates. Reka Albert and Albert-Laszlo Barabasi studied a highly connected network model which was later called the scale-free network. â€Å"Networks have become a general tool for describing the structure of interaction or dependencies in such disparate systems as cell metabolism, the internet, and society.† (Barabasi A-L, Albert R 2002) With scale free networks, even in very large networks, nodes can be selected arbitrarily and connected through other nodes which serve as the intermediary nodes. â€Å"There are features that the scale-free network contains that are lacking in the random network. In a scale free network, a small number of nodes contribute heavily to connectivity. These nodes are called hubs. In a random network , each node contributes approximately the same to the overall connectivity of the network.†(Barabasi, Albert-Laszlo 2002) In a scale-free network, the network is self-similar, in that different parts of the network are statistically similar throughout the entire network. This self similarity is a major feature of fractals. â€Å"The term "scale-free" was first coined by physicist Albert-Laszlo Barabasi and his colleagues at the University of Notre Dame in Indiana. In 1998, they mapped the connectedness of the World Wide Web and found, to their surprise, that the web did not have an even distribution of connectivity (so-called "random connectivity"). Instead, a very few network nodes (also referred to as hubs) were far more connected than other nodes. In general, they found that the probability P (k) that a node in the network connects with k other nodes was, in a given network, proportional to k. They named this kind of network connectivity "scale-free". They also argued that there is a simple explanation for this behavior. Many networks expand through the addition of nodes to an existing network, and those nodes attach preferentially to nodes already well-connected. When this is the case, a scale-free network naturally arises.† (Watts, D.W 2003) Although a scale-free netw