code: def net_fluxes(sources, sinks, msm, for_committors=None):
      
  
      flux_matrix = fluxes(sources, sinks, msm, for_committors=for_committors)
  
      net_flux = flux_matrix - flux_matrix.T
      net_flux[np.where(net_flux < 0)] = 0.0
  
      return net_flux
docs: Computes the transition path theory net flux matrix.
  
      Parameters
      ----------
      sources : array_like, int
          The set of unfolded/reactant states.
      sinks : array_like, int
          The set of folded/product states.
      msm : msmbuilder.MarkovStateModel
          MSM fit to data.
      for_committors : np.ndarray, optional
          The forward committors associated with `sources`, `sinks`, and `tprob`.
          If not provided, is calculated from scratch. If provided, `sources`
          and `sinks` are ignored.
  
      Returns
      -------
      net_flux : np.ndarray
          The net flux matrix
  
      See Also
      --------
      fluxes
  
      References
      ----------
      .. [1] Weinan, E. and Vanden-Eijnden, E. Towards a theory of
             transition paths. J. Stat. Phys. 123, 503-523 (2006).
      .. [2] Metzner, P., Schutte, C. & Vanden-Eijnden, E.
             Transition path theory for Markov jump processes.
             Multiscale Model. Simul. 7, 1192-1219 (2009).
      .. [3] Berezhkovskii, A., Hummer, G. & Szabo, A. Reactive
             flux and folding pathways in network models of
             coarse-grained protein dynamics. J. Chem. Phys.
             130, 205102 (2009).
      .. [4] Noe, Frank, et al. "Constructing the equilibrium ensemble of folding
             pathways from short off-equilibrium simulations." PNAS 106.45 (2009):
             19011-19016.