Here's a set of actions demonstrating how to achieve the kind of geometry referenced in the second image in your post.
Shift+A : To add bezier curve
Tab : To go into edit mode
W : To go to specials menu, and set curve radius to 0. This isn't strictly required
W : Specials menu again, and subdivide
Select alternate vertices and delete. The subdivision and deletion is actually the same as rotating originally created bezier circle 45 degrees.
Repeat following steps
for each branch that needs to be extruded from the intersection node-
X : Delete a segment
E : Extrude loose vertices (x2) twice
F : Close the open ends of the loose vertices with a segment
V : To set the handle type of the control points making the end segment to 'Vector'
Then, after the branches are created-
Select the four original vertices from the initially created bezier, and Ctrl+X to dissolve vertices
Select all vertices other than the end segment 'vector' ones and set handle type to 'Vector'
Select only the handles which you want to see rounded and change handle type to 'Aligned'
Tab : Step out of edit mode)