Applications of Graph Theory in Healthcare Sector

Graph theory is a very natural and powerful tool in combinatorial research. Some necessary research issues particularly inventory control problem that may be resolved using graphs. It suggests the chances that exist for improving the operational, military science and strategic decision-making of health care inventory systems through the employment of graph theory approaches. This blog aims to boost the attention of health care managers and inventory researchers with relevance to realistic graph theory applications.

Overview

• Graph theory introduction
• Graph theory in real world problems 
• Google maps 
• Graphs in Healthcare system
• EHR System
• Conclusion

Graph theory introduction :

Graph theory may be a mathematical sub-field of discrete mathematics. In graph theory, we have tendency to study graphs, which might be accustomed to describe pairwise relationships between objects. Graph theory was created in 1736, by the mathematician Leonhard Euler.

Graph with five vertices and seven edges

The graph in above figure contains five vertices (the numbered circles) and seven edges (the lines connecting the vertices). Vertex four is adjacent to the vertices one, 2, and 3. Thus, the vertices three and four are neighbors. The edge (3,4) is incident to the vertices three and four and is also incident to the edges (1,3), (1,4), and (2,4).


Graph theory in real world problems :

Graphs are the ultimate abstraction for many real world issues and today, technology exists that can treat them as such. A graph is a data structure which stores data in the form of a collection of interconnected vertices (nodes) and edges (paths). Graphs are great data structures that we use every day through Google Maps, GPS, Google Search and social media. They are used to represent entities that share connections. Some of the best applications of Graph Data Structures are in; Web Analytics and Scientific Computations, Path Optimization Algorithms such as Car Navigations and Google Maps Platform (Maps, Routes APIs) ,  Social Graph APIs such as Facebook's Graph API, Recommendation Engines such as Yelp's GraphQL API.

Google maps :

Google uses algorithms to find the best routes. In order for these algorithms to work correctly, they need a proper form of input. Let us first consider what concept should be applied to the problem of finding the shortest path so that it makes the most sense.

Let the set of edges be denoted by E and the set of vertices by V. For each edge e∈E we denote its edge weight by ce. 

In the case of a road network, the edge weights represent the time it takes to go from one vertex u to its neighbour v via the edge {u,v}, which represents a road that leads from u to v.

The task of finding the shortest way from point A to point B can thereby be reduced to finding the shortest path on a weighted graph. There are a lot of different algorithms that can do this but Google Maps most likely uses A∗ search.

Graphs in Healthcare system :

Have you ever wondered how Graph theory contributes to the Healthcare Sector? One of the uses is , using Google maps to track nearby hospitals(Healthcare centres) at a less familiar place. Several apps could be made, such as apps that could contact blood donors in nearby area so blood could be made available easily at the time of emergency.
Aarogya Setu app : 

Let’s not go far, we can take the example of present situation. Right now we are all fighting the life threatening corona virus. India is gearing up to launch an app to help users check if they have been in close contact with people infected with the coronavirus. The app is called Aarogya Setu (also CoWin-20), and is currently being tested on both iOS and Android. It will track your location and alert you if you are near a COVID-19 infected patient. CoWin-20 will use your location data and Bluetooth to gauge if you’ve been near a person who was infected by COVID-19. It likely determines that by looking through a database of people who have been infected, as well as with one containing individuals’ travel history. It’s also said to be able to tell you if you’re in an area with a high number of coronavirus cases. Most of the data here is stored with the help of graphs.

EHR System :

Graph is an appropriate data structure for modelling objects' interactions. Graph theory is a well-established area of mathematics that also covers methods to compare graphs. Apart from graph databases, these methods make the usage of graphs in medical context very interesting, for example to model patient data of EHR (Electronic Health Record) systems. With approaches like this, diagnoses, therapies and medications could be suggested on the basis of previous patients and the experiences made at treatment of these patients. Such a system could also be part of a decision support system for physicians in clinical context. For example, graphs are used for spatial description of cerebral anatomy or for clustering of patients and for making a diagnosis . Other approaches are closer related to EHR. Such projects focus for example on visualizing collaborative electronic health record usage with heart failure , modelling disease graphs or to predicting knowledge graphs of unknown adverse drug reactions .


Conclusion :

Graphs are almost everywhere in more places then you think it is. The world is highly interconnected, and graph databases aim to mimic those sometimes-consistent, sometimes-erratic relationships in associate intuitive manner. That’s what makes the graph paradigm completely different than other database models. It maps a lot of realistically to however the human brain maps and processes the globe around.


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