We use the WHα versus [N ii]/Hα (WHAN) diagram introduced by us in previous work to provide a comprehensive emission‐line classification of Sloan Digital Sky Survey galaxies. This classification is able to cope with the large population of weak line galaxies that do not appear in traditional diagrams due to a lack of some of the diagnostic lines. A further advantage of the WHAN diagram is to allow the differentiation between two very distinct classes that overlap in the low‐ionization nuclear emission‐line region (LINER) region of traditional diagnostic diagrams. These are galaxies hosting a weakly active galactic nucleus (wAGN) and ‘retired galaxies’ (RGs), i.e. galaxies that have stopped forming stars and are ionized by their hot low‐mass evolved stars. A useful criterion to distinguish true from fake AGN (i.e. the RGs) is the value of ξ, which measures the ratio of the extinction‐corrected Hα luminosity with respect to the Hα luminosity expected from photoionization by stellar populations older than 108 yr. We find that ξ follows a markedly bimodal distribution, with a ξ≫ 1 population composed by systems undergoing star formation and/or nuclear activity, and a peak at ξ∼ 1 corresponding to the prediction of the RG model. We base our classification scheme not on ξ but on a more readily available and model‐independent quantity which provides an excellent observational proxy for ξ: the equivalent width of Hα. Based on the bimodal distribution of WHα, we set the practical division between wAGN and RGs at WHα= 3 Å. Five classes of galaxies are identified within the WHAN diagram: pure star‐forming galaxies: and WHα > 3 Å; strong AGN (i.e. Seyferts): and WHα > 6 Å; weak AGN: and WHα between 3 and 6 Å; RGs (i.e. fake AGN): WHα < 3 Å; passive galaxies (actually, lineless galaxies): WHα and W[N ii] < 0.5 Å. A comparative analysis of star formation histories and of other physical and observational properties in these different classes of galaxies corroborates our proposed differentiation between RGs and wAGN in the LINER‐like family. This analysis also shows similarities between strong and weak AGN on the one hand, and retired and passive galaxies on the other.

A numerous population of weak line galaxies (WLGs) is often left out of statistical studies on emission‐line galaxies (ELGs) due to the absence of an adequate classification scheme, since classical diagnostic diagrams, such as [O iii]/Hβ versus [N ii]/Hα (the BPT diagram), require the measurement of at least four emission lines. This paper aims to remedy this situation by transposing the usual divisory lines between star‐forming (SF) galaxies and active galactic nuclei (AGN) hosts and between Seyferts and LINERs to diagrams that are more economical in terms of line quality requirements. By doing this, we rescue from the classification limbo a substantial number of sources and modify the global census of ELGs. More specifically, (1) we use the Sloan Digital Sky Survey Data Release 7 to constitute a suitable sample of 280 000 ELGs, one‐third of which are WLGs. (2) Galaxies with strong emission lines are classified using the widely applied criteria of Kewley et al., Kauffmann et al. and Stasińska et al. to distinguish SF galaxies and AGN hosts and Kewley et al. to distinguish Seyferts from LINERs. (3) We transpose these classification schemes to alternative diagrams keeping [N ii]/Hα as a horizontal axis, but replacing Hβ by a stronger line (Hα or [O ii]), or substituting the ionization‐level sensitive [O iii]/Hβ ratio with the equivalent width of Hα(WHα). Optimized equations for the transposed divisory lines are provided. (4) We show that nothing significant is lost in the translation, but that the new diagrams allow one to classify up to 50 per cent more ELGs. (5) Introducing WLGs in the census of galaxies in the local Universe increases the proportion of metal‐rich SF galaxies and especially LINERs. In the course of this analysis, we were led to make the following points. (i) The Kewley et al. BPT line for galaxy classification is generally ill‐used. (ii) Replacing [O iii]/Hβ by WHα in the classification introduces a change in the philosophy of the distinction between LINERs and Seyferts, but not in its results. Because the WHα versus [N ii]/Hα diagram can be applied to the largest sample of ELGs without loss of discriminating power between Seyferts and LINERs, we recommend its use in further studies. (iii) The dichotomy between Seyferts and LINERs is washed out by WLGs in the BPT plane, but it subsists in other diagnostic diagrams. This suggests that the right wing in the BPT diagram is indeed populated by at least two classes, tentatively identified with bona fide AGN and ‘retired’ galaxies that have stopped forming stars and are ionized by their old stellar populations.