Eye diagram (for baseband transmission) shows how many levels the transmission has and hence the bits/symbol of the system.
If you know the shaping of the transmission,
spectral_efficiency [bits/s/Hz] = symbol_efficiency [bits/symbol] / spectral_occupancy [Hz / (symbol/s)]
For instance, if the eye pattern of a baseband NRZ transmission has 4 levels, you have a symbol_efficiency of 2 bits/symbol; if it would use minimum bandwidth (i.e. strctly limited to 1/(2T)) meaning spectral_occupancy of 0.5 Hz/(symbol/s), then the spectral efficiency would be 1 bits/s/Hz. Other shaping (e.g. raised-cosine with roll-off factor > 0) increases spactral occupancy and decreases spectral efficiency.
Sometimes, the term "eye diagram" is used instead of "constellation diagram" for passband APSK transmission. In this case, the relationships are the same but you must consider the number of points instead of the number of levels, and the fact that the spectrum is two-sided around the carrier.
Regards
Z