  Webs are weighted sets of Feynman diagrams which build up the logarithms of
correlators of Wilson lines, and provide the ingredients for the computation of
the soft anomalous dimension. We present a general analysis of multiple gluon
exchange webs (MGEWs) in correlators of semi-infinite non-lightlike Wilson
lines, as functions of the exponentials of the Minkowski cusp angles,
$\alpha_{ij}$, formed between lines $i$ and $j$. We compute a range of webs in
this class, connecting up to five Wilson lines through four loops, we give an
all-loop result for a special class of diagrams, and we discover a new kind of
relation between webs connecting different numbers of Wilson lines, based on
taking collinear limits. Our results support recent conjectures, stating that
the contribution of any MGEW to the soft anomalous dimension is a sum of
products of polylogarithms, each depending on a single cusp angle, and such
that their symbol alphabet is restricted to $\alpha_{i j}$ and $1 - \alpha_{i
j}^2$. Finally, we construct a simple basis of functions, defined through a
one-dimensional integral representation in terms of powers of logarithms, which
has all the expected analytic properties. This basis allows us to compactly
express the results of all MGEWs computed so far, and we conjecture that it is
sufficient for expressing all MGEWs at any loop order.

High Energy Physics - Phenomenology;High Energy Physics - Theory