Find the graph from binary image

Hi all,i have binary image as below

i found the branching points using this code

[I,J]= find(  bwmorph(BW,'branchpoints') );

i need to find the graph below automatically? is there any way to find it?

[navanit dubey]

how did you marked the branching points in image

i mean I want to know how should I show it in matlab?