We then proceed to connect these mentions i) if they co-occur within the same document (we will refer to this as DOC-BASED edges), ii) if the pair of named entity mentions is identical (MATCH edges—these may connect nodes across and within documents), or iii) if they are in the same coreference chain, as predicted by the external coreference system (COREF edges). 
 Question: Did they use a relation extraction method to construct the edges in the graph?
No