2021-019

Which of the formulas below computes the average degree of an undirected network, where \( N \) is the number of nodes in the network,  \( k_i \) is the degree of node \( i \), \( N_k \) is the number of degree-\(k\) nodes, and \( A \) is the adjacency matrix:

1. $$ \sum_{j=1}^N A_{j,i} $$
2. $$ \dfrac{1}{2} \sum_{i=1}^N k_i $$
3. $$ \dfrac{1}{N} \sum_{i=1}^N k_i $$
4. $$ \dfrac{N_k}{N} $$
5. None of the above

Original idea by Mauricio Schiezaro