Equation for "importance" value of twitter user according to #followers #following

I am trying to find an equation which calculates the "importance" of a twitter user according to #following #followers

Things I want to consider:

1. The more #followers / #following is bigger, the more important he his.

2. differ between 20/20 and 10k/10k (10k is more important although the ratio is the same).

Considering these two, I expect开发者_运维知识库 to get a similar output importance value to these two inputs:

#followers=1000 #following=100

#followers=30k #following=30k

I'm having problems inserting the second point into consideration. I believe it needs to be quite simple. Help?

Thanks

one possibility is (#followers/#following)*[log(#followers) - CONST] where CONST is some predefined value, tested as appropriate. this will ensure the ratio has its appropriate importance, but also the scale matters.
for your last example, you will need to set CONST~=9.4 to achieve similar results.

There are too many answers to this question, you need to weight how important is the number of followers compared to the ratio so you get a common number to relationate this two. For example the first idea that come to my mind is to multiply the ratio by the log of the #Followers. Something like this.

Importance = (#Followers / #Following)*Log(#Followers)

Based on what you said there, you could do 3*followers^2/following.

But you've described a system where users can increase their importance by following fewer other users. Doesn't seem too awesome.

You could normalize it by the total number of users.
I'd suggest using logarithms on all the values to get a less dramatic increase or change in higher values.

(log(#followers)/log(#TotalNumberOfPeopleInTwitter))*(log(#followers)/log(#following))