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Graph Theory, Research Paper Example

Pages: 1

Words: 1640

Research Paper

Abstract

Graph theory is the study of graphs which shows a relational impact between different areas, functions, entities or other catalysts.  The graph is a model representation of the relationships or processes and provides a practical representation of dynamic information.  Specifically in the representation of networks the graphs can represent communication models, data organization, information flow and computations and logic relationships.  The application of graph theory spans multiple areas of study such as mathematics, biology, sociology and computer sciences.  One key area for utilization of graph theory is in the development of a knowledge management system and the development of how that knowledge is transferred across networks.  The development of those networks takes resources to plan, configure, implement, monitor and control.  Assigning these resources requires tools to ensure effectiveness and efficiency are established.  Within computer science networking is increasing in importance due to the exponential growth in demand for connectivity and the need for efficiency and security of those networks. There are many examples of utilizing graph theory in computer networks such as providing the framework for optimization of the network in terms of connectivity, reliability and efficiency.

Areas of Application Overview

Within computer science there are many areas that benefit from the implementation of the graph theory.  By showing relationships, defining dependencies and allowing a representation of the effectiveness and the opportunity for optimization, the graph theory provides a tool for ensuring security, determining data flow, processing data into information and planning network paths and allocating resources.  The areas of focus for the practical application of graph theory include knowledge management systems which require interrelated networks of data and the security of that data specifically focused on wireless networks.

Knowledge Management System Development

There are many challenges when developing a knowledge management system.  When developing or implementing any new idea or project there are hurdles that the project team will encounter that span outside of the viability and functionality that the project is going to provide  There are outside factors that could present themselves as obstacles but understanding those challenges can turn those obstacles into opportunities.  These challenges include factors such as the culture of the people providing the knowledge as well as those accepting the knowledge, value of the knowledge, the orchestration and preparation of the knowledge for consumption and use as well as the integration and flow of knowledge for full implementation for the end users.

To understand the challenges of the knowledge management system life cycle it is first critical to understand what knowledge management is and what encapsulates its lifecycle.  The knowledge management’s purpose is to package knowledge from subject matter experts regarding key systems, processes, procedures, experiences or insights and provide that knowledge to others within the organization (Hislop 2009).

There are three key areas that provide a basis for the knowledge that is in the knowledge management system.  These three areas provide a challenge due to the fact that if any are neglected the system would become antiquated and unusable.  These areas are data accuracy, interpretation and relevancy (Becerra-Fernandez, Sabherwal, and Gibson).  The first is data accuracy which means that the knowledge or data that is inputted into the system must be accurate and ultimately reliable.  The challenge is ensuring the accuracy and maintaining the level of effort required for validation of the data.  The next is the ability for the information to be interpreted by the user.  The data that is inputted into the knowledge management system must be able to be meaningful and usable to the end user.  Without usable information the system will fail.  Lastly of the three, the relevance is critical.  This falls in line with obsolete information and the power of the data relies on how up-to-date the data is and how it relates to the knowledge required by the end user.  Managing these three areas is a challenge to the knowledge management system because without a focus on all three of these areas the system would not be utilized to its intended purpose.

Networking in Computer Science-Data Security

With the ever increasing reliance on wireless networks there are more opportunities for risks to data by external forces trying to take advantage of the security weaknesses of a wireless network.  There are many threats to wireless networks and many of these risks can cause damage to the organization’s and customers’ data.  The first type of attack would include gaining access by going right into the network.  Without the proper security measures an intruder could gain access to the wireless network by sniffing out the wireless signal and logging into the system which grants access to key data and business information.  These types of attacks can be active or passive.  The active attack is where the intruder is actively seeking out ways to intrude into the network and there is also passive ways for malicious entities to hinder a network.  The active risks include direct access to an authorized network access, network hijacking, denial of service and flooding the network with unnecessary requests which limits the ability for the network to be used (Hayden, 2010).  The passive attacks utilizes software programs to seek out unsecured or weakly secured networks and accesses them through the program to gain access and cause a disruption.  These attacks can be limited and reduced with the appropriate network security measures such as password protection, encryption and other software and hardware security measures.  Through the use of the graph theory key security areas are identified and can easily have resources assigned to address the potential security issues.  This documentation allows the graphical representation of the security network to become more of a security tool than a diagram of security points in the network.

Graph Theory

Graph theory is used to represent in a graphical representation a group of relational items.  The purpose of this graphical representation is to show a direct correlation between items and how they link together.  This is important in the application of graph theory in the computer science field of study specifically in the area of networks and how the network sends and receives data from one point to the next.  The graphs are used to model not only the relationships between the processes and data flow but also the dynamic effects each point in the process has upon the preceding and future points in the process.  There are two areas that are specific to graph theory that provide assistance in developing the area of networks in the field of computer science.  These areas are flow network and Max-flow min-Cut theorem.  These are focused on key areas of a network in regard to flow and capacity as well as efficiency and optimization.

The flow network is a directed graph, a graph that has a specific direction associated to it, that has a specific capacity or capability in which each edge of the graph can operate (van Steen, 2010).  This capacity defines limits in which the flow can operate and provides not only a visual awareness to areas that can be monitored and controlled to adjust the network to function properly but also ensure that resources are properly allocated to maintain the appropriate level of capacity at each edge.  In networking the flow diagram would allow the insight into data flow from one area to another and would determine areas that are exceeding capacity or other areas that have too many resources allocated and provides more capacity than required by the system.

The Max-flow min-Cut theorem is an optimization function of the graph theory that represents the max flow of a system or network (van Steen, 2010).  This show the total amount of data, in the case of a knowledge management network, that can be processed at any given time.  This type of information would also provide the key inputs into how a network can be optimized or integrated into an overall security plan to ensure efficiency, effectiveness, security and reliability of the system is optimized.

The overall purpose of the graph theory is not to provide every facet of network development or ensure every security measure is taken but to provide a tool to raise the awareness of key points of opportunity and avoid those key points of failure that would not normally have the awareness without the graphical representation allotted by the graph theory’s use.

Graph theory has advanced the knowledge and understanding in both development of the knowledge management systems and network security by allowing contextual visualization on key points within each of the systems as a whole.  The implementation of a knowledge management system requires an infrastructure built on a network designed to perform to a specific set of parameters while avoiding information choke points and restrictions that are caused by specific areas in the network.  These areas can be determined through the max-flow min-cut theorem to show where additional capacity should be accomplished or where resources providing capacity that is not require could be reallocated to level out the total capacity of the system to allow adequate data flow.

Conclusion

Graph theory’s application has practical use in the development of secured networks and the capacity management of knowledge management systems that base their utilization on the networks in which they are housed.  The foundation of a secure system and an effective and efficient network is enhanced through the use of flow network and Max-flow min-Cut theorem.  These areas allow the continual improvement of the network to right-size the limited resources based on the outputs of the graph theory.   Capacity management, resource utilization, maximum flow and security optimization are all benefits of the graph theory.

References

Becerra-Fernandez, I., R. Sabherwal, and C. F. Gibson. (2010). Knowledge management : Systems and processes. Armonk: Sharpe Incorporated. Print

Hayden, L. (2010). It security metrics. New York: McGraw Hill.

Hislop, D. (2009). Knowledge management in organizations: A critical introduction. 2nd. New York : Oxford University Press. Print

van Steen, M. (2010). Graph theory and complex networks: an introduction. Amsterdam: Maarten van Steen. Retrieved from http://www.distributed-systems.net/index.php?id=graph-theory-and-complex-networks

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