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values on an edge may include zero, MatlabBGL optionally returns the edges and values explicitly as a set of “(source, destination, value)” triplets.10 Graph outputs are returned as sparse adjacency matrices. Finally, when the output is a rooted tree, we store it as a single array where the ith entry gives the parent of vertex i in the tree. Matlab already uses this storage format for elimination trees of sparse matrix algorithms (see treeplot). Weighted trees, from prim_minimum_spanning_tree for example, are returned as triplet arrays or sparse matrices. This section concludes our description of the common Matlab to Boost graph library interface that exists in MatlabBGL. The next few subsections discuss some extensions of this standard interface to take advantage of more of the Boost graph library. 6.3.5 An in-place class for visitors The Boost graph library implements “visitors” to make its algorithms flex- ible. Visitors are small classes whose methods are triggered by events in an algorithm. They enable reuse for an implementation of a simple graph algorithm in a more complicated algorithm. One example is the strong_¬ components function. Using a visitor, it reuses the existing depth_first_¬ search implementation. An alternative use of the visitor pattern is to collect additional information about an algorithm while it is running. One example of this feature is recording the first visit “time” for a vertex in a breadth-first search. Another example is stopping a search algorithm when it reaches a target vertex. Inside the BGL, these visitors are C++ classes that the algorithm calls at various points. In MatlabBGL, we pass in a set of function handles to receive the calls instead. Historically, Matlab functions would not have been able to be full featured visitors in the BGL as they could not store information within a function call like a C++ class. (We did not consider using global variables for this task an acceptable solution.) From Matlab version 7, however, Matlab supports functions that maintain state using nested functions and closures. These tools are the keys to making visitors useful in MatlabBGL.11 We explain this by way of a small example. 10 The libmbgl code always returns triplet arrays and users get the option of which form to view the triplet arrays in the MatlabBGL calls 6.3 ⋅ matlabbgl 125 11 From Matlab 2008a, the new class semantics support yet another way of constructing visitors in Matlab.PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY
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