Graph theory in mathematics is a section which deals with the study of graphs. These graphs are mathematically structured and are used to model and relate pairwise relation in solids. Mathematical graphs are made up of points, nodes, and vertices’ which may be connected by lines, arc or edges. Graph theory has greatly contributed positively to the field of mathematics since its first discovery and formulation by the famous Swiss mathematician Leonhard Euler (1707-1783). This was the beginning of the graph theory. This resulted when Leonhard Euler wanted to find a nice path between seven bridges. Graphs are classified into different categories; all these have applications in different fields (Ali et.al, 2017). Examples include isomorphic, counting, bipartite and representing graphs. Another person to come up with a project on graph theory was Sir William Rowan Hamilton (1805-1865), he developed a device based on getting a path through all cities once.
Graphs have been a crucial technique in describing several phenomena in the real world. These graph theory applications are used to give the simple description of events or datasets such as to give a more helpful understanding of more detailed data. This has contributed to analyzing of BIM devices based on IFC standard. The birth in the more advanced form of graph model called labeled property graphing ( Biggs et.al, 1986 ) . To simplify the graph: it’s made up of nodes and interrelations that are expressed in vertices and corners. Labeling these graphs will give the additional properties to facilitate understanding. For this reason, the nodes will have one or more multiple labels. The relations between the nodes and edges will give a graph. This is achieved by connecting two nodes each at start and end. There have been several graph theories developed within the last ten years. This has led to various advancements that meet the modern modeling using graph. Doekemeijer & varbanescu, 2014-PDS-2014-003 revealed that more than 80 inventions were introduced within 2004-2014. Graph theory has been applied in database systems to perform analysis of data. Other importance includes data storage in more advanced and efficient way. The main merits of graph theory to database systems can simply be summarized as below.
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Graph theory has had its applications in database systems. An example is advanced analyzing of Building information models based on industry foundation classes standard. The concept has its positive implications for time management and fast data retrieval services.
The three main applications of graph theory are as follows
Used to give the simple description of events or datasets such as to give a more helpful understanding of more detailed data. This can be achieved through graph models
Efficient data storage- this can be achieved using special graph storage algorithms and structures
Applications of graph theories in data management
The choice and utilization of this theory will solely depend on individual/company priority to how it wants to manage its data. The first two applications indicated above are more important, and those are the ones am going to discuss.
Data modeling
Data modeling is the analysis and comparison of data using models. This model could be objects or physical shapes and conceptualized designs. Graph theory has necessitated various ways in which data is represented. Modeled data is easier to understand than any other form of data representation. A modeled data has specific path; this path is easily compatible with other data models if they have used the same format. It’s easy to share data if they have the same structure, this inhibits cyberbullying and crimes hence less threat to the systems ( West, 2001 ).
A typical example of model data can appear as follows
Organization
Example of modeled data.
Operationally, graphs can be stored efficiently within databases using special graph storage structures, and functional graph algorithms for application of specific operations.
Data storage is one of the most crucial parts of data management in every institution.
To store data, one has to ascertain that the data meets the following for efficiency
Space utilization – having data occupying more space means costly and high resources need. This involves cloud backups, hard disks, floppy disks among other available storage facilities. These facilities are easier to maintain if they could be in small scale.
Easy access- not bulkier means more reliable work, and this makes it possible for anytime time usage even with minimal time.
Security-a secure data management is one of the reasons why graph theory is used. A system can only access data stored in graphs with the same structure as the one available in the institution. It will be difficult for one to access the files if he she has no clue of the structure. Hence it’s more secure to use graphs.
Integrity controls-not everyone guaranteed permit to a database system can decode the data, this makes it necessary for the institution to use decode tools only accessed by high integrity personals.
Analyzing data stored in the graph is easier. This is because every person can easily interpret graphs with vision and even less knowledge of data.
The above graph chart has been used to represent a database system. This graph when stored will occupy less space, more secure and easily analyzed in this form unlike when raw data is kept.
This advancement in graph theory has much impact in mathematics field, the major area being database systems management. The major impacts and advancement advantages are highlighted below.
Less time in handling data.
Easy analyzing data
Automation-through programming of graphical data
Less human interaction in data systems
Priority management
Reduced statistical methods use.
In conclusion, Scientist Euler successful attempt at realizing the graph theory has it's implicated widely known. This is as discussed above. In my field, graph theory has made it possible for easy management of data systems. Mathematics has many fields, different philosophers have had many theories to solve various problems, the graph theory is one of them, and its major application I will utilize in achieving the following. My applications to graph theory will be majorly out cased in the following areas
In data analyzing
Representing statistical data
Queries development
Modeling data and
For general knowledge use. These applications in mathematics tally with the discrete mathematics, both finite and infinite.
References
Ali, Ahmed N, Raimar Scherer Dresden (2017). Application of graph databases and graph theory concepts.
Biggs, N.; Lloyd, E.; Wilson, R. (1986), Graph Theory, 1736–1936, Oxford University Press.
Ismail, A., Nahar, A., & Scherer, R. Application of graph databases and graph theory concepts for advanced analysing of BIM models based on IFC standard.
West, D. B. (2001). Introduction to graph theory (Vol. 2). Upper Saddle River: Prentice Hall
