title: Algorithm for classification of vertices in a graph based on their weight
body: <p>I have the following complete weighted graph, where each weight represents the probability of a vertice belonging to the same category as the next. I know a priori the category for which some of the vertices belong to; how would I be able to classify every other vertice?</p>
  
  <p><a href="https://i.stack.imgur.com/L5BtM.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/L5BtM.jpg" alt="image"></a></p>
  
  <p>In a more detailed manner I can describe the problem as following; From all the vertices N and clusters C, we have a set where we know for sure the specific cluster which a node belongs: P(v_n|C_n)=1. From the graph given we also know for each node, the probability of every other belonging to the same cluster as it: P(v_n1∩C_n2). From this, how can we estimate the cluster for every other node?</p>