There are some people who immediately look for another relationship: that's not for me.
DH was a good bit older than me and told me that he wanted me to "get another man" once he was gone.
I have a friend who is very keen on finding another partner for herself, but that's not something I'm looking for. It's been more than five years for me.
I was fairly astonished that DH's ex quickly found a new partner after the death of each of her partners. (Including DH, to whom she was married for some time, she's on partner number 4. I think she's had less than a year between men.)
Now that I'm on my own, I've discovered that it's laughably easy to find another man - and I'm no oil painting. I'm not interested: I now avoid speaking to men my age, by and large, in order to avoid misunderstandings.
I had one situation where (presumably a decent enough chap) thought that I was chatting him up when I just thought that I was having a conversation: he noticed my wedding ring, made a comment and ended the conversation.
I was embarrassed and nearly blurted out "I'm a widow!" but didn't want to give him the wrong idea, so bit my tongue. It's easier just to avoid the situation.