3 research outputs found
Extremal linkage networks
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with max-stable distribution. The fitness determines the node attractiveness w.r.t. incoming edges as well as the spatial range for outgoing edges. For max-stable fitness distributions, we thus obtain a complex spatial network, which we coin extremal linkage network.</p
A spatial small-world graph arising from activity-based reinforcement
In the classical preferential attachment model, links form instantly to newly
arriving nodes and do not change over time. We propose a hierarchical random
graph model in a spatial setting, where such a time-variability arises from an
activity-based reinforcement mechanism. We show that the reinforcement
mechanism converges, and prove rigorously that the resulting random graph
exhibits the small-world property. A further motivation for this random graph
stems from modeling synaptic plasticity.Comment: 9 pages, 1 figur