Gephi -- Spline

A spline is a smoothed curve used for interpolation.[1]

In data visualization programs we frequently map a range of colors or sizes to a range of data values. We might, for example, have a graph in which vertex degree varies from 1 to 27 and we want to display this with vertex symbols ranging from size = 2.0 to size =10.0.

The simplest approach would be to say size(1) = 2 and size(27) = 10, draw a straight line between them, calculate its slope

(1)
\begin{align} slope = \frac {size(27) - size(1)} {27 - 1} = \frac {10-2} { 27-1} = 0.307 \end{align}

and then the y-intercept, b, (that is, size(degree=0)) can be calculated from $slope = 0.307 = \frac {2-b} {1-0}$ to yield b=1.69. Thus

(2)
\begin{align} size (degree) = 0.307 \times degree + 1.69 \end{align}

as seen here:

But what if we wanted to emphasize, visually, the differences among the lower degree nodes and were not too concerned about the difference between nodes with degree 23, 25, or 27? Then we might use a non-linear spline that changes node size more rapidly in the lower ranges and less so as we approach the maximum degree in the graph.

The use of splines for coloring rankings is similar.

The Gephi spline editor lets you create a custom curve or pick from several built-in curves.

### References

Bibliography
1. Wikipedia. Spline (mathematics).
2. Wikipedia. Spline interpolation