Graphs are most useful when encoding extended data across levels and complex multivariate relationships.
The 1915 Standards for Graphic Presentation identify ‘multidimensionality’ as the most important quality of data graphs given their ability to quickly and accurately impart and interpret complex information.
On the other hand, if data is limited, then graphical display is likely to be irrelevant and the data could be best displayed in a table or just narrated.
Multidimensional graphs draw links, encourage comparison, describe causal relations and unveil aggregation levels (the so-called macro/micro view of data). Multidimensional graphs require several iterations and careful design particularly from the data management stage. For example, relationships may need to be represented as differences, or aggregated into levels, or reduced to statistical summaries, and so on.
Data become more and more complex by the day, in terms of its volume, dimensions and connections, and data graphs are indispensable tools for helping us understand the drivers of this data complexity.
In this regard, data reduction techniques are indispensable tools in data graphing for sieving out random noise from complex stochastic data and extracting useful signals. As an examples of simplifying complexity using data reduction see my analysis on the market value function.