A BRIEF ANALYSIS ABOUT GRAPH THEORY

MATHEMATICS

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pair wise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges So many things in the world would have never come into existence if there hadn’t been a problem that needed solving. This truth applies to everything, but boy, is it obvious in the world of computer science. So, which amazing abstraction shall we learn about next? Well, now that we’re experts in tree data structures, it only seems right to understand where trees came from. Trees are actually a subset of something you might have already heard about: graphs. But in order to truly know why we use graphs and what they are, we’ll need to go deep down to the very roots of something that stems from discrete mathematics: graph theory. If this is your very first foray into discrete math, fear not it’s mine, too! Let’s tackle it together and try not to lose our sanity in the process. When we first started looking at non-linear structures, we learned about their most fundamental characteristic: that their data doesn’t follow an order at least, not an obvious numerical one, like we see in arrays or linked lists. Trees, as we learned, start with a root node, and might connect to other nodes, which means that could contain subtrees within them. Trees are defined by a certain set of rules: one root node may or may not connect to others, but ultimately, it all stems from one specific place. Some trees have even more specific rules, like binary search trees, which can only ever have two links to two nodes at any given time.

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