sum of degrees
Table of Contents
sum of all nodes’ degress equals to 2m (each link have 2 end, and is thus counted twice when adding degrees of all nodes together) \[ \sum_V\text{deg}v=2m \]
Backlinks
network metrics
(network)
- sum of degrees
- average degree
- c-dense and c-sparse
- diameter of network
- measuring homophily
modularity
- Notation
- \(A_{i,j}\) is entry in adjacency matrix of node i and node j
- \(\delta(c(i),c(j)\) returns 1 if \(i\) and \(j\) is of the same class, and 0 if \(i\) and \(j\) is of different classes
- \(m\) - number of links, (\(2m\) is also sum of degrees)
- definition \[ Q = \frac{1}{2m}\sum_{i,j}(A_{i,j} - \frac{\text{deg} i * \text{deg} j }{2m} )\delta(c(i),c(j)) \]
average degree
devide sum of degrees by number of nodes \[ \bar d_G = \frac{1}{n}\sum_V\text{deg}_Gv \] or equivalently, \[ \bar d_G = \frac{2m}{n} \]