Graphs play an important part in intelligent technologies such as recommendation engines, search engines, fraud detection applications, network mapping, customer journey applications, latency evaluation and dependency management. Graphs data structures are also powerful in social networks such as Twitter, Facebook, LinkedIn and a few others. Graphs in the context of the social graph are used to recommend friends, events, company pages, jobs and personalise the ad experience. These are some of the use cases of graph data structures and applications. 

A quick reminder of the definition, graphs are considered to be the composition of vertices (nodes) with respective pairs of edges(also known as links or arcs). In a nutshell, they are viewed to comprise a determined set of nodes and edges which connect these given nodes. 

The example below adapted from GeekforGeeks indicates 5 nodes {0,1,2,3,4} and 7 edges {01,12,23,34,04,31,13,14}

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