Graph Theory — Basic Properties

We’ll now circle back to highlight the properties of a simple graph in order to provide a familiar jump-off point for the rest of this article.simple graph — part I & II exampleIn the previous article, we defined our graph as simple due to four key properties: edges are undirected & unweighted; the graph is exclusive of multiple edges & self-directed loops..The image below provides a quick visual guide of what our example graph were to look like if it contained weighted edges:Multiple Edges & LoopsThe third our simple properties highlighted in our example graph introduces two separate graph relationships that are both based off the same property: the simplicity of the graph based on vertex relationships.In our example graph, each vertex has exactly one edge connecting it to another vertex — no vertex connects with another vertex through multiple edges..A graph that does contain either or both, multiple edges & self-loops, is known as a multigraph.The image below highlights these two distinctions with the graph on the right:Cycles — Acyclic vs Cyclic GraphsWe didn’t list this property earlier on because both acyclic & cyclic graphs can count as simple graphs, however, the cyclical property of a graph is a key form of classification that’s worth covering..In our example below, we’ll highlight one of many cycles on our simple graph while showcasing an acyclic graph on the right side:Having now covered a basic understanding of key properties associated with graphs, it’s time to make a leap to a much exciting topic with graph theory: networks!. More details

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