where Z ( α ) denotes ∑ L r = $_{1}$r − $^{α}$. Obviously, ( $^{a}$− 1)(2log2 + log Z ( a )) + a + 1 2( $^{a}$− 1) 2 is a monotonic increasing function. Thus, for any fixed c , -1 is the optimal exponent. 

## VI. ABOUT THE EVOLUTIONARY MODEL (EM) 

## A. Why we chose new friend only from the next nearest neighbors? 

There are 2 reasons. The first is that, according to our real so cial experience, we always make some new friends who are the friends of our friends. The second is that EM is a global optimal algorithm. Thus if we choose any node as our new friend, the result will be the same theoretically. 

## B. How to Measure the Power Law Exponent in EM? 

To accurately measure the exponent value of power law distribution is not a easy work. Es- pecially, when the exponent is very close to − 1. We use the least square method to evaluate the exponent value. We are afraid the least square method is not a good way, so we plot the accu- mulated curve. Fortunately, it can be proved that when P ( r ) ∝ r − $^{1}$, the accumulated function in log-linear plot will be a straight line. We can see that the distribution is about P ( r ) ∝ r − $^{1}$. 

[1] Liben-Nowell, D., Novak, J., Kumar, R., Raghavan, P. and Tomkins, A. Geograph routing in social networks. Proc. Natl. Acad . 102 , 11623-11628 (2005). 

[2] http: // www.calit2.net / newsroom / article.php?id = 1558 and the up coming book: Christakis and Fowler: Connected: The Surprising Power of Social Networks and How They Shape Our Lives, Little Brown, (2009). 

