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The topology of the Grid: Connectivity

Summarizing some critical consequences:

the Network Monitoring topology depends on network
performance. In fact if the basic assumption -- internal better than
external -- fails, Network Monitoring returns partially invalid data;
the Characteristic (or metric) used to design the topology must
be one, therefore valid for all applications (unless we want a
topology for distributed computing, one for massive transfers, one for
playback applications etc.);
the Characteristic used to design the topology should be static
(like **capacity**),
or change only in response to exceptional events (failures,
reconfigurations);
internal paths should be monitored (not necessarily published),
in order to detect the occurrence of exceptional events.
Let's call **Connectivity** the metric choosen for
designing the topology of Network Monitoring.

Degrees of freedom in the choice of the **Connectivity**
function:

it is not necessarily a distance (triangular inequality etc.);
it may be a-dimensional (dB);