Counting the sum of every nodes’ neighbors’ degrees?

For each node u in an undirected graph, let twodegree[u] be the sum of the degrees of u’s neighbors. Show how to compute the entire array of twodegree[.] values in linear time, given a graph in adjacency list format.

This is the solution

for all u ∈  V :
  degree[u] = 0
  for all (u; w) ∈  E:
    degree[u] = degree[u] + 1
for all u ∈  V :
  twodegree[u] = 0
  for all (u; w) ∈  E:
    twodegree[u] = twodegree[u] + degree[w]

can someone explain what degree[u] does in this case and how twodegree[u] = twodegree[u] + degree[w] is supposed to be the sum of the degrees of u’s neighbors?

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