Classes of Graphs used in Biology
I don't think there is a single "class of graph" that isn't used in biology.

In biology (just like in any other natural science), we have all kind of data types;


non-ordinal variables
boolean
ordinal categorical
numeric
tree data
other types of network data
pure functions (from statistical or theoretical models)
pictures
sounds
etc..


We make all kind of graphs out of these data;


scater plot
points or lines with eventually error bars
bar graphs with eventually error bars
kites
boxplot
images (colored shaped kind of things; e.g. density maps)
phase diagrams
multidimensional graphs
pie charts
function graphs
Venn diagrams
existential graphs
flow diagrams (incl. alluvial diagrams, spankey diagrams, ...)
trees
matching trees
other types of networks
schematic representations
pictures
spectrograms
videos
interactive graphs
etc...


One can really display any kind of data / information in anyway (s)he wants to.

Kite graphs are just simple graphs to compare frequencies variation along a continuous variable and among a categorical (ordinal or not) variable. It isn't the most common types of graphs but we see them. As a matter of fact, in a paper of mine that is currently under revision the figure 1 is a kite graph (with nested non-ordinal categorical variables).

Just look at random papers to find graphs. Go on google.scholar.com and search for any biology subject and you'll find papers with graphs.