l-independence of nodes. Sketch of a generic graph, with node A at the center. The first, second and third neighbors of node A are respectively located within the yellow, pink, and gray region. The l-independent set of a graph is the set of nodes such that the distance between any two of them is larger than l. The black nodes (A, B, C and D) form the 2-independent set of the graph, as all of them are at a distance larger than 2 from each other. The black nodes together with the ones depicted in light blue form, instead, the 1-independent set. Note that the light blue nodes do not participate in the 2-independent set. Finally, the red nodes belong neither to the 1-independent set nor to the 2-independent set.

Contexts in source publication

Context 1

... can now generalize the latter definition, and designate as a l-independent set S l the set of network's nodes such that the distance between any pair of its members is larger than l [13]. It follows that nodes belonging to S l do not necessarily belong to S l+1 (see Fig. 2 for an illustrative sketch of the comparison between a 2-independent set and a classical 1-independent ...

Context 2

... the number of alternative shortest paths may be very large in large sized networks, the minimum possible benefit obtained from gluing a 1-independent set (as node 7 would do by forming edges with nodes 1 and 2) may be very small with the growth of When only black links are considered, vertices 1,2,7 form a 1-independent set. For consistency with Fig. 2, nodes 1 and 2 are colored in light blue. As vertex 7 forms the yellow edges (7,1) and (7,2) it is removed from the 1-independent set (this change is depicted by coloring the lowest part of the node in yellow), but the two new connections do not remove nodes 1 and 2 from the 1-independent set, since they only contribute to the ...