In many real-world applications data appear to be sampled around 1-dimensional
filamentary structures that can be seen as topological metric graphs. In this paper we …

Let $ G $ be a connected graph with the usual shortest-path metric $ d $. The graph $ G $ is
$\delta $-hyperbolic provided for any vertices $ x, y, u, v $ in it, the two larger of the three …

The (Gromov) hyperbolicity is a topological property of a graph, which has been recently
applied in several different contexts, such as the design of routing schemes, network …

Let $ G $ be a connected graph with the usual shortest-path metric $ d $. The graph $ G $ is
$\delta $-hyperbolic provided for any vertices $ x, y, u, v $ in it, the two larger of the three …

Given a graph, its hyperbolicity is a measure of how close its distance distribution is to the
one of a tree. This parameter has gained recent attention in the analysis of some graph …

Let G be a connected graph, and let d (a, b) denotes the shortest path distance between
vertices a and b of G. The graph G is δ-hyperbolic if for any vertices a, b, c, d of G, the two …

If X is a geodesic metric space and x 1, x 2, x 3∈ X, a geodesic triangle T={x 1, x 2, x 3} is
the union of the three geodesics [x 1 x 2],[x 2 x 3] and [x 3 x 1] in X. The space X is δ …

The Gromov hyperbolicity is an important parameter for analyzing complex networks which
expresses how the metric structure of a network looks like a tree. It is for instance used to …

If $ X $ is a geodesic metric space and $ x_1, x_2, x_3\in X $, a geodesic triangle $ T=\{x_1,
x_2, x_3\} $ is the union of the three geodesics $[x_1x_2] $, $[x_2x_3] $ and $[x_3x_1] $ in …

Let $ G $ be a graph with the usual shortest-path metric. A graph is $\delta $-hyperbolic if for
every geodesic triangle $ T $, any side of $ T $ is contained in a $\delta $-neighborhood of …