Visualization techniques are very useful in data analysis. Their aim is to summarize information into a graph or a plot. In particular, visualization is especially interesting when one has functional data, where there is no total order between the data of a sample. Taking into account the information provided by the down–upward partial orderings based on the hypograph and the epigragh indexes, we propose new strategies to analyze graphically functional data. In particular, combining the two indexes we get an alternative way to measure centrality in a bunch of curves, so we get an alternative measure to the statistical depth. Besides, motivated by the visualization in the plane of the two measures for two functional data samples, we propose new methods for testing homogeneity between two groups of functions. The performance of the tests is evaluated through a simulation study and we have applied them to several real data sets.