We study a photonic band gap (PBG) material consisting of multiple waveguides. The multiconnected waveguides provide different paths for direct wave interference within the material. Using coaxial cables as waveguides, we are able to tune the PBG of the material. Using direct destructive interference between different paths of the waveguides, we experimentally observe a kind of PBG which is quite different from the traditional PBG that is caused by scattering in dielectrics with inhomogeneous refractive indices. Particularly, this newly observed PBG has an extremely strong wave attenuation, making electromagnetic (EM) waves in the PBG cannot even pass through one unit cell under certain conditions. We also systematically investigate the transmission of EM waves in our PBG materials and discuss the mechanism of band gap formation. Our results provide a new insight to develop new band gap materials for photons and phonons.