graph - what is the lowelink mean of Tarjan's algorithm -

I was reading the details to find strongly connected components in a dry graph. But I find it hard to understand the code snippet:

  if (w.index is undefined) // has not yet been reached to achieve success; Recurse at this: strongconnect (w) v.lowlink: = minutes (v.lowlink, w.lowlink) else if (in WS), then the successor is in w heap S. and hence in the current SCC v.lowlink: = minimum (V.lowlink, w.index) end if   
 The fourth and seventh lines are different, it confuses me. And in my opinion, the seveth line can be written in the same way with the fourth line  v.lowkink: = minutes (v.lowlink, w.index)   
 I This test works well in my program, and for me, it is better that access to BCZ Wadex and Cloud has reached the root, but I could not do it IT_T   
 
 
 i) a program that enumerates all the graphs of size 4, then each version (either  Minutes (run with v.lowlink, w.index  or written  minutes (v.lowlink, wlowlink)  if in ws) and compared to results. Were similar, though wlowink and w.index were often different.  
 Due to the fact that we can use the w index: consider where the stack S is in relation to the current and The node is the W v node.  
 If it is first on the heap, then it is a small indicator compared to the current node (because it was previously visited, oh), so the current node is not "head" its Related component and this v.lowlink & lt; = w.index & lt; V.index anyway and it does not like w.lowlink has any special meaning at this point, it is in progress of being calculated and The essential is not yet its final value.  
 Now, if W is later in the heap, compared to V In, depending on the algorithm, the important asset is that then there is a descendant of Y, some brother / cousing node will still not leave the first recursive call. Or, as is usually said in a complete proof, strongly connected components are never many unrelated branches of our search tree (forest). Since this is an SCC, since there should be a way from th to v, and since we are calculating the goods in a deep-first order, then before we finish the process, we use v Must be visited, so W should be in the pile than before!  
 And if we are descendants of the left, we have already received the actual Kamlink value when we first saw it and there is no interest in it.  
 On one side, note that the Kamlink property is comparable to getting rid of the nodes and return the strong connect directly to the connector. After this we will not take the exam to examine it instead of w.index in the second case =)