Saddle points, Nodes and Edges definitions

I am working on some algorithm implementation, however being new to image processing, I have some questions about some of the definitions used. UPDATE: for those asking for more information, this is the RELEVANT information stated in the paper.

"Step 4: Centerline Computation Our implementation of the centerline extraction is based on the Distance Transform with thinning as post-processing step as proposed by niblack. The result is a binary mask image g with a centerline thickness of 1, which corresponds to the undirected edge image graph." Then :

• They(in the paper) keep on mentioning a node without prior definition, this means a truepoint with 2 other trueneighbors(out of 8). Am I right ? (this is the general definition of a node pixel)

• They define an Edge being the distance between two adjacent nodes where the distance between them is $\leq \sqrt2$. What do they mean by that exactly ?

• Last they define saddle points being node pixels with the connected edge length has to be $\geq 3$. I don't know what they mean by that