Applications of Graph Theory

Graph Theory is used in vast area of science and technologies. Some of them are given below:

1. Computer Science

In computer science graph theory is used for the study of algorithms like:

• Dijkstra's Algorithm
• Prims's Algorithm
• Kruskal's Algorithm

• Graphs are used to define the flow of computation.
• Graphs are used to represent networks of communication.
• Graphs are used to represent data organization.
• Graph transformation systems work on rule-based in-memory manipulation of graphs. Graph databases ensure transaction-safe, persistent storing and querying of graph structured data.
• Graph theory is used to find shortest path in road or a network.
• In Google Maps, various locations are represented as vertices or nodes and the roads are represented as edges and graph theory is used to find the shortest path between two nodes.

2. Electrical Engineering

In Electrical Engineering, graph theory is used in designing of circuit connections. These circuit connections are named as topologies. Some topologies are series, bridge, star and parallel topologies.

3. Linguistics

• In linguistics, graphs are mostly used for parsing of a language tree and grammar of a language tree.
• Semantics networks are used within lexical semantics, especially as applied to computers, modeling word meaning is easier when a given word is understood in terms of related words.
• Methods in phonology (e.g. theory of optimality, which uses lattice graphs) and morphology (e.g. morphology of finite - state, using finite-state transducers) are common in the analysis of language as a graph.

4. Physics and Chemistry

• In physics and chemistry, graph theory is used to study molecules.
• The 3D structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms.
• Statistical physics also uses graphs. In this field graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems.
• Graphs are also used to express the micro-scale channels of porous media, in which the vertices represent the pores and the edges represent the smaller channels connecting the pores.
• Graph is also helpful in constructing the molecular structure as well as lattice of the molecule. It also helps us to show the bond relation in between atoms and molecules, also help in comparing structure of one molecule to other.

5. Computer Network

• In computer network, the relationships among interconnected computers within the network, follow the principles of graph theory.
• Graph theory is also used in network security.
• We can use the vertex coloring algorithm to find a proper coloring of the map with four colors.
• Vertex coloring algorithm may be used for assigning at most four different frequencies for any GSM (Grouped Special Mobile) mobile phone networks.

6. Social Sciences

• Graph theory is also used in sociology. For example, to explore rumor spreading, or to measure actors' prestige notably through the use of social network analysis software.
• Acquaintanceship and friendship graphs describe whether people know each other or not.
• In influence graphs model, certain people can influence the behavior of others.
• In collaboration graphs model to check whether two people work together in a particular way, such as acting in a movie together.

7. Biology

• Nodes in biological networks represent bimolecular such as genes, proteins or metabolites, and edges connecting these nodes indicate functional, physical or chemical interactions between the corresponding bimolecular.
• Graph theory is used in transcriptional regulation networks.
• It is also used in Metabolic networks.
• In PPI (Protein - Protein interaction) networks graph theory is also useful.
• Characterizing drug - drug target relationships.

8. Mathematics

In mathematics, operational research is the important field. Graph theory provides many useful applications in operational research. Like:

• Minimum cost path.
• A scheduling problem.

9. General

Graphs are used to represent the routes between the cities. With the help of tree that is a type of graph, we can create hierarchical ordered information such as family tree.