Francorachel/ Thank you.
RebYidd – you’re right about you specifically inviting a woman to dine, but for people who have both husband AND wife at home, it is nice to include people who are alone, whoever they may be, male or female, with or without children. Only twice in 37 years have I not asked someone back for a second meal, and in both cases the guest acted inappropriately either in my home or elsewhere that I observed, and I therefore felt uncomfortable with hosting that person again. I am not saying we have to invite divorcees, widows and their male counterparts to EVERY meal, but it is thoughtful and sensitive to recognize that they are probably very lonely, and would like the companionship of others for a yom tov, if not Shabbos meal.
BTW, to all the divorced or widowed men and women – it would not hurt for YOU to invite other people in your same boat, or even the people who have hosted you, to come for a meal at your house sometime, or if money is tight, offer to do something nice for them, like babysit, or the like. (No, I am not suggesting the men should do this). When there is some measure of reciprocity, it could help alleviate the feeling that some people might have of being a “nebach” if they are contributing positively to the relationship.