An ego network begins with a single individual (“ego”) and asks that individual to identify his, her (or its) network contacts (“alters”). In a 1.0 level ego network, the process stops there. See here for a d3js.org visualization of 1.0 level ego networks of airports in 2008, the connections to other cities possible from any city’s airport.
In a 1.5 level ego network, we find out which of ego’s alters are connected to one another, but we don’t ask if ego’s alters are connected to anybody who isn’t one of ego’s alters.
Below is a 1.5 level ego network. Ego is the black node.
In a 2.0 level ego network, we engage in full snowball sampling to find out the full set of alters’ own alters, regardless of whether alters’ alters are connected to ego.
Below is a 2.0 level ego network, again with ego as the black node (dotted lines indicates steps outward in the snowball sampling process).