Using spectroscopy from the Sloan Digital Sky Survey Data Release Seven , we systematically determine the electron density n _ { e } and electron temperature T _ { e } of active galaxies and star-forming galaxies while mainly focusing on the narrow-line regions ( NLRs ) .
Herein active galaxies refer to composites , low-ionization narrow emission-line regions ( LINERs ) and Seyferts following the Baldwin-Phillips-Terlevich diagram classifications afforded by the SDSS data .
The plasma diagnostics of n _ { e } and T _ { e } are determined through the I [ S II ] \lambda 6716/ \lambda 6731 and I [ O III ] \lambda 5007/ \lambda 4363 ratios , respectively .
By simultaneously determining n _ { e } from [ S II ] and T _ { e } from [ O III ] in our [ O III ] \lambda 4363 emission sample of 15 019 galaxies , we find two clear sequences : T _ { LINER } \gtrsim T _ { composite } > T _ { Seyfert } > T _ { star - forming } and n _ { LINER } \gtrsim n _ { Seyfert } > n _ { composite } > n _ { star - forming } .
The typical range of n _ { e } in the NLRs of active galactic nuclei ( AGNs ) is 10 ^ { 2 - 3 } cm ^ { -3 } .
The temperatures in the NLRs range from 1.0 to 2.0 \times 10 ^ { 4 } K for Seyferts , and the ranges were even higher and wider for LINERs and composites .
The transitions of n _ { e } and T _ { e } from the NLRs to the discs are revealed .

We also present a comparative study , including stellar mass ( M _ { \star } ) , specific star formation rate ( SFR/M _ { \star } ) and plasma diagnostic results .
We propose that Y _ { L } \gtrsim Y _ { SY } > Y _ { C } > Y _ { SF } , where Y is the characteristic present-day star-formation time-scale .
One remarkable feature of the Seyferts shown on an M _ { \star } -SFR/M _ { \star } diagram , which we call the evolutionary pattern of AGN with high ionization potential , is that the strong [ O III ] \lambda 4363 Seyferts distribute uniformly with the weak Seyferts , definitely a reverse of the situation for star-forming galaxies .
It is a natural and well-known consensus that strong [ O III ] \lambda 4363 emissions in star-forming galaxies imply young stellar populations and thus low stellar masses .
However , in the AGN case , several strong lines of evidence suggest that some supplementary energy source ( s ) should be responsible for high ionization potential .