  The strength of forward-backward (FB) multiplicity correlations is measured
by the ALICE detector in proton-proton (pp) collisions at $\sqrt{s}=0.9$, 2.76
and 7 TeV. The measurement is performed in the central pseudorapidity region
($|\eta| < 0.8$) for the transverse momentum $p_{\rm T}>0.3$ GeV/$c$. Two
separate pseudorapidity windows of width ($\delta \eta$) ranging from 0.2 to
0.8 are chosen symmetrically around $\eta=0$. The multiplicity correlation
strength ($b_{\rm cor}$) is studied as a function of the pseudorapidity gap
($\eta_{\rm gap}$) between the two windows as well as the width of these
windows. The correlation strength is found to decrease with increasing
$\eta_{\rm gap}$ and shows a non-linear increase with $\delta\eta$. A sizable
increase of the correlation strength with the collision energy, which cannot be
explained exclusively by the increase of the mean multiplicity inside the
windows, is observed. The correlation coefficient is also measured for
multiplicities in different configurations of two azimuthal sectors selected
within the symmetric FB $\eta$-windows. Two different contributions, the
short-range (SR) and the long-range (LR), are observed. The energy dependence
of $b_{\rm cor}$ is found to be weak for the SR component while it is strong
for the LR component. Moreover, the correlation coefficient is studied for
particles belonging to various transverse momentum intervals chosen to have the
same mean multiplicity. Both SR and LR contributions to $b_{\rm cor}$ are found
to increase with $p_{\rm T}$ in this case. Results are compared to PYTHIA and
PHOJET event generators and to a string-based phenomenological model. The
observed dependencies of $b_{\rm cor}$ add new constraints on phenomenological
models.
