Device-to-device (D2D) communication allows serving local wireless traffic bypassing the system's infrastructure. One way to control the interference in D2D networks is to carefully channelize transmissions. This paper presents an analytical characterization of ITLinQ, one of the principal D2D channelization schemes proposed to date. Recognizing that it captures well the spatial characteristics of D2D networks, a stochastic geometry setting is utilized for this analysis. The derived expressions enable gleaning insights on how ITLinQ avoids situations of excessive interference, and they facilitate optimizing the controllable parameters of ITLinQ so as to maximize the system spectral efficiency (bits/s/Hz per unit area). With the parameters thus optimized, the ultimate performance of ITLinQ can be evaluated with respect to other D2D channel allocation schemes. In particular, performance evaluation comparisons with the FlashLinQ scheme are provided, and the gains with respect to an unchannelized network are quantified.