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connected nodes

I am working on text analytics and building a knowledge graph with high frequency entities (noun chunks) as graph nodes and their linkage between co-occurrence in a sentence as edges.

I am able to get the information about no. of degrees (N) of freedom for every node and information about nodes and their linkages.

for ex:

for A node N = 8
for B node N = 4
for all other nodes, N = 1

So as the nodes are getting propagated, i.e, when nodes C,D,E,F,G,H,I,J,K,L are forming linkages with other new nodes going further, I want to give more associative weightage to A and B nodes.

To keep it simple, I want to assign more weightage to nodes (like A&B) which are linked to other nodes which are not end nodes.

Also the associative weightage of nodes C,D,E,F,G,H,I,J,K,L also should be increased as the new linkages are getting formed.

I'm researching on ways to assign associative weightages to highly connected nodes as the knowledge graph is increasing in size. Any help or suggestion regarding techniques would be helpful.

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