Before getting into “applications of graph theory in day to day life”, you must be aware of graph theory.

#### What is Graph Theory?

Graph Theory is nothing but the connection of vertex with one or several edges. Mathematically we can define by pair of sets of vertices and edges. i.e G=(V,E). Besides all of these, we also have loops, parallel edges, degrees, isolated vertex. For these, you can check our other posts on Graph Theory.

First of all, you need to understand, everything in this world is linked. Just like all cities are linked by highway, webpages are linked by hyperlinked in the internet, components of the electric device, and networks of network services or transportation. The *application of graph in daily life* is really intriguing.

## Applications of graph theory in day to day life

Graph Theory is used for many purposes and used by almost every field of interest. Graphs are used in the field of medical, criminology, or be it as a small schoolboy problem of spreading rumors. How viruses are spread across borders or cities are also able to find using graph theory. So, let’s check in detail the applications of graph theory in day-to-day life.

Inside the fields of Biology and Medicine, the expected uses of organization investigation by utilizing chart hypothesis incorporate distinguishing drug targets, deciding the job of proteins or qualities of obscure capacity. There are a few natural areas where diagram hypothesis methods are applied for information extraction from the information.

### #1.Applications of graph theory in the field of Internet

In the web Search engine like Google, It searches for web pages, where pages on Internet are linked to each other by hyperlinks. The web pages and sites are connected by the graph help to rank pages and allow google to display the best page. Connecting the friends on social media, where each user is vertex and when users connect they create an edge.

### #2.Applications of graph theory in Traffic

The transportation network is very important for communication structure which supports air and road transportation Air traffic control organize the air spaces to achieve the objective of a safe and orderly flow of traffic To reduce traffic problem To develop Perfect road transport system

### #3. How to use graph in solving a crime

Third but the most most important Application of graph theory in day-to-day life. As you known graph theory is all about linking and the study of linking. It can help you to find the one who spread the wrong rumor in a classroom to a mastermind of a serious crime.

FBI investigations years ago a graph was created that includes the terrorists involved in the 9/11 attacks and how they were connected what they did and what we’re about to do is mathematically determine who the key people in this network are and who should have been prioritized by law enforcement.

It might be hard to see who law enforcement should prioritize but if we calculate those three scores for every node and rank the results we find what our eyes could probably not that one person shows up at the top of each list and his node can be found here and it turns out this person was one of the ringleaders of the entire 9/11 plot.

Although this was unfortunately found out after the fact graph theory still singled out one person mathematically who would have provided a lot of information that US intelligence had he been caught beforehand and whether it be terrorist organization street gangs or a bioterrorist attack and how a disease will spread graph theories being used by law enforcement criminologist mathematicians and so on every single day to track and prevent crime.

Someone is committing crimes throughout the LA area on a regular basis maybe they’ve committed five crimes in the last month at these locations how could we go about catching this person one thing we can do is try finding a pattern in prime locations in order to make a prediction about the next one that can be tricky though since there’s likely a huge element of randomness.

But decades ago Kim Rossmo Ph.D. criminologist had another idea he tried to find a formula which was an application of graph theory, that instead could find where the criminal likely lives based on past data he knows that criminals often don’t commit crimes right by their own home but also they don’t go too far away so from the data you can determine a quote hot zone which isn’t too close or too far from the crime scenes it has a high probability of the person living there this is his equation for determining those probabilities I know it looks complex but it’s actually not as bad as you think like.

And we create a heat map of probability what you’re seeing here actually is the output of the equation based on real crimes of a serial killer from the 70s named Richard chase you can see the crime locations in green and the formula predicts his residence to be somewhere in this dark region his actual residence is plotted here in purple exactly as expected so at least in this case Rossmo’s formula works his formula was put to use in the 90s and successfully caught a serial rapist making Rossmo a celebrity in the crime-fighting world.

Then for anyone who’s a fan of the American tv show “numbers,” you may recognize all this in the first episode, there’s a scene where Charlie Eppes a mathematician looks out of the window at a sprinkler and says although he couldn’t determine where the next drop will land he could figure out where the sprinkler head is located or the point of origin he then tells his brother who worked for the FBI that he can determine where serial killer lives using the same analysis later in the episode you see him working with Rossmo’s exact formula and the heat map that had generated.

There are much more applications of graph theory that we might miss in this article. Please mail to us at “mathdart@gmail.com” if you want to tell us more about this topic.