You use specific words to describe graphs formally. The "things" or "points" in the graph are called Vertices (singular: Vertex). Some books call them Nodes.
In a social network, each person is a vertex. In a map, each city is a vertex. In a computer network, each device is a vertex.
When you read graph problems, you will see " vertices" or " nodes." These mean the same thing. The number of vertices determines the size of your data structures. If , you might need arrays of size . Knowing vertex count upfront helps you estimate memory usage.