Graph theory Research Paper Example | Topics and Well Written Essays - 500 words

Graph theory - Research Paper Example iss Mathematician developed a solution to an old puzzle related to the possibility of establishing a path across every one of the seven bridges that span a forked river flowing past (Biggs 140). From a conceptual perspective, a graph is formed by vertices and edges linking the vertices. From a formal perspective however, a graph refers to a pair of sets (V, E), where V is a set of vertices and E is a set of edges. Based on these fundamental concepts underpinning graph theory, this paper seeks to explain the importance and application of the theory’s theoretical concepts in various fields (Biggs 124). The concept of graph theory is important because graphs allow for a simplification of complex concepts, eliminating the irrelevant details without forfeiting much information necessary for the task. As asserted by Biggs (148), the assumptions made by the graph theory match the real world conditions and are therefore not comparable to any other model. Among the fundamental uses of the graph theory entail; giving a unified formalism for diverse looking real life problems. This has been the sufficient basis upon which algorithms have been presented in this common formalism. The theoretical concepts underpinning graph theory are widely used in the studying and modeling of various applications, in diverse fields. These include; construction of bonds in chemistry, study of molecules, and the study of atoms. Graph theory is widely used in Sociology for instance to measure the prestige of actors or in exploring the mechanisms of diffusion (Biggs 150). Besides, the conservation efforts made in biological sciences essentially apply the concepts of graph theory where a vertex represent regions where certain species exist and the edges are used to represent paths of migration or movement from one region to another (Biggs 152). Such information is important more so when examining the breeding patterns or tracking the spread of parasites, diseases and in the study of the

Black Water security and what they do in Iraq as security contractors Essay

Black Water security and what they do in Iraq as security contractors - Essay Example Blackwater is one of the most high profile private security firms working in Iraq. Blackwater Worldwide along with its subsidiaries, Blackwater Training Center, Blackwater Target Systems, Blackwater Security Consulting and Blackwater Canine is engaged in the task of providing security to American officials in Iraq, in keeping with the company’s aim of employing a â€Å"new generation of capability, skills, and people to solve the spectrum of needs in the world of security† (Blackwater Security.com.) The services the company renders, include providing security for the American military bases, the Green Zone, infrastructure, weapons demolition, cash transport, guarding important military, civilian and government dignitaries, gathering of intelligence, covert operations, psychological warfare, and most importantly, training Iraqi security forces. (Government Accountability Office, Rebuilding Iraq: Actions Needed to Improve Use of Private Security Providers (July 2005) (GAO-05-737).) Being the security provider for sensitive and important officials of the government and also the military, Blackwater personnel have to often engage in fights with the locals and in one such incident in Baghdad on September 16, 2007, 14 Iraqi civilians and 18 others were wounded, while escorting a convoy through the city. This incident pushed the company into the limelight and it has had to face some hard truths about the way in which it is running its operations in Iraq. The government of USA has been able to increase the number of ground staff by employing private security operatives. This has helped them to maintain the troop levels on the ground without resorting to draft. These private security operators are a part of a ‘shadow army’ which is better trained and equipped than some of the militaries of many countries. In August 2003, Blackwater officially became the security provider for the U.S. civilian