Abstract — Arigatoni is a structured multi-layer overlay network that provides various services with variable guarantees, and promotes an intermittent participation in the overlay because peers can appear, disappear, and organize themselves dynami-cally. Arigatoni provides a very powerful decentralized, asyn-chronous, and scalable resource discovery mechanism within an overlay with a dynamic network topology. In the first version of Arigatoni, the network topology was tree- or forest-based. This paper makes a significant step by weaving the network topology with general dynamic graph properties. As an immediate conse-quence, the Arigatoni protocols must be reconsidered in order to take into accounts routing loops when updating routing tables, for dealing with resource overbooking, and resource discovery loops. Index Terms — Overlay networks, resource discovery, virtual organizations, dynamic graphs, peer-to-peer, global computing,