code: def _fraction_visited(source, sink, waypoint, tprob, for_committors,
                        cond_committors):
      
  
      fraction_visited = (np.float(tprob[source, :].dot(cond_committors)) /
                          np.float(tprob[source, :].dot(for_committors)))
  
      return fraction_visited
docs: Calculate the fraction of times a walker on `tprob` going from `sources`
      to `sinks` will travel through the set of states `waypoints` en route.
  
      Computes the conditional committors q^{ABC^+} and uses them to find the
      fraction of paths mentioned above.
  
      Note that in the notation of Dickson et. al. this computes h_c(A,B), with
          sources   = A
          sinks     = B
          waypoint  = C
  
      Parameters
      ----------
      source : int
          The index of the source state
      sink : int
          The index of the sink state
      waypoint : int
          The index of the intermediate state
      tprob : np.ndarray
          Transition matrix
      for_committors : np.ndarray
          The forward committors for the reaction sources -> sinks
      cond_committors : np.ndarray
          Conditional committors, i.e. the probability of visiting
          a waypoint when on a path between source and sink.
  
      Returns
      -------
      fraction_visited : float
          The fraction of times a walker going from `sources` -> `sinks` stops
          by `waypoints` on its way.
  
      See Also
      --------
      msmbuilder.tpt.conditional_committors
          Calculate the probability of visiting a waypoint while on a path
          between a source and sink.
      msmbuilder.tpt.hub_scores : function
          Compute the 'hub score', the weighted fraction of visits for an
          entire network.
  
      References
      ----------
      .. [1] Dickson & Brooks (2012), J. Chem. Theory Comput., 8, 3044-3052.