Barabasi-Albert-Zuckerberg

Computer Science Level 3

If people did join Facebook in the way modeled by a Barabasi-Albert graph and the average path length with 721 million users was 4.74, what would the average path length between two users be in 2016 with 1.59 billion users? (Round your answer to two decimal places.)


The answer is 4.92.

Adam Strandberg by Adam Strandberg , 28, USA

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1 solution

Adam Strandberg
Feb 17, 2016

Since the average path length for a Barabasi-Albert network is roughly proportional to log N \text{log} N , we have

4.74 = k log 7.21 ∗ 1 0 8 4.74 = k \text{log} 7.21 * 10^{8} k = 0.535 k = 0.535

So the new average path length L L is

L = 0.535 log 1.79 ∗ 1 0 9 = 4.92 L = 0.535 \text{log} 1.79 * 10^9 = 4.92

Note that it doesn't matter what base we use for the logarithm in this solution since logarithms in different bases differ by a multiplicative factor that is absorbed in k k .

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