Apart from very special cases, there is no single way to draw a graph and visualize it. Indeed, graphs are most often an abstract representation of reality. For instance, all four graphs depicted in the following image represent the exact same set of nodes and edges, so, by definition, the same mathematical graph:
We cannot rely only on our eyes to find patterns within graphs. For instance, looking only at the lower-right plot, it would be impossible to see the pattern that is visible in the upper-right plot. That's where graph algorithms enter into the game, which will be discussed in more detail in Chapter 6, Node Importance, and Chapter 7, Community Detection and Similarity Measures.
