Is Twitter Count… do the math

August 8, 2010

Here is a very interesting piece of research by HP that has the dubious tittle of “influence and Passivity in Social Media” and what is go on with twitter This is not a report for the faint hearted or for the die hard Twitterers and twitter-ets that post millions of short comments every day.

ABSTRACT

The ever-increasing amount of information ﬂowing through Social Media forces the members of these networks to compete for attention and inﬂuence by relying on other people to spread their message.

An evaluation performed with a 2.5 million user data-set shows that our inﬂuence measure is a good predictor of URL clicks, outperforming several other measures that do not explicitly take user passivity into account. We also explicitly demonstrate that high popularity does not necessarily imply high inﬂuence and vice-versa.

Later in the paper you will have fun math like this to check out.

For every arce = (i, j)∈E, we deﬁne theacceptance rate

byuij =

wi,j

k:(k,j)∈E

wkj

This value represents the amount of inﬂuence that userj accepted from useri normalized by the total inﬂuence accepted byj from all users on the network. The acceptance rate can be viewed as the dedi- cation or loyalty userj has to useri. On the other hand, for everye = (j, i)∈E we deﬁne therejection rate by

vji=

1−wji

k:(j,k)∈E

(1−wjk ). Since the value 1−wji is amount of inﬂuence that useri rejected fromj, then the valuevji represents the inﬂuence that useri rejected from userj nor- malized by the total inﬂuence rejected fromj by all users in the network.

Hope you like it because my brain is hurting…