Thoughts and concepts on exploring, visualizing, and measuring distances on networks

The properties of data networks are determined by routing protocols, link delays, traffic demands, and similar system parameters, which are not directly connected to the formal topology of the network\´s graph. Consequently, two different links, or source-destination (SD) pairs, could appear close in the network\´s topological layout, and yet be far apart when measured on the "functionality scale" of traffic flow. We present our own ideas regarding distance functions for network objects, the type of data that can be collected to determine such distances, and applications in network visualization, exploration, and monitoring, and in network tomography. This short paper is not intended as a survey of the topic but rather narrowly focuses on our own current thoughts on the topic