(Quiz week 5, sep 15th, Question 1) Consider the table took from Barábasi's book, chapter 3 (http://networksciencebook.com/chapter/3#small-worlds):

\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Network} & \text{N} & \text{L} & \text{$\langle k \rangle$} & \text{$\langle d \rangle$} & \text{$d\ max$} & \text{lnN/ln$\langle k \rangle$}\\ \hline Internet & 192,244 & 609,066 & 6.34 & 6.98 & 26 & 6.58\\ \hline WWW & 325,729 & 1,497,134 & 4.60 & 11.27 & 93 & 8.31\\ \hline Power\ Grid & 4,941 & 6,594 & 2.67 & 18.99 & 46 & 8.66\\ \hline Mobile-Phone\ Calls & 36,595 & 91,826 & 2.51 & 11.72 & 39 & 11.42 \\ \hline Email & 57,194 & 103,731 & 1.81 & 5.88 & 18 & 18.4 \\ \hline Science\ Collaboration & 23,133 & 93,437 & 8.08 & 5.35 & 15 & 4.81\\ \hline Actor\ Network & 702,388 & 29,397,908 & 83.71 & 3.91 & 14 & 3.04\\ \hline Citation\ Network & 449,673 & 4,707,958 & 10.43 & 11.21 & 42 & 5.55\\ \hline E.\ Coli\ Metabolism & 1,039 & 5,802 & 5.58 & 2.98 & 8 & 4.04\\ \hline Protein\ Interactions & 2,018 & 2,930 & 2.90 & 5.61 & 14 & 7.14\\ \hline \end{array} \]

Comparing data from the table, judge the statements bellow:

1. We can see Small World phenomena at Internet and Mobile-Phone Calls networks.
2. We cannot see Small World phenomena at Power Grid and Protein Interaction networks.
3. We can nearly see Small World phenomena at Actor Network network.

The correct statements are:

1. Only I.
2. Only II.
3. Only III.
4. Only I and III.
5. None of the above.

Original idea by: Fábio Assunção.