  We use gravitational waves (GWs) from binary black holes (BBHs) and neutron
stars inspiraling into intermediate-mass black holes to evaluate how accurately
the future space-based GW detectors such as LISA, Taiji and TianQin and their
combined networks can determine source parameters and constrain alternative
theories of gravity. We find that, compared with single detector, the detector
network can greatly improve the estimation errors of source parameters,
especially the sky localization, but the improvement of the constraint on the
graviton mass $m_g$ and the Brans-Dicke coupling constant $\omega_{BD}$ is
small. We also consider possible scalar modes existed in alternative theories
of gravity and we find the inclusion of the scalar mode has little effect on
the constraints on source parameters, $m_g$, and $\omega_{BD}$ and the
parametrized amplitude $A_B$ of scalar modes are small. For the constraint on
the graviton mass, we consider both the effects in the GW phase and the
transfer function due to the mass of graviton. With the network of LISA, Taiji
and TianQin, we get the lower bound on the graviton Compton wavelength
$\lambda_g\gtrsim 1.24 \times 10^{20}$ m for BBHs with masses
$(10^6+10^7)M_\odot$, and $A_B< 5.7\times 10^{-4}$ for BBHs with masses
$(1+2)\times 10^5M_\odot$; $\omega_{BD}>6.11\times10^{6}$ for neutron
star-black hole binary with masses $(1.4+400)M_{\odot}$.
