Collaboration: people, papers, average graphs, Durfee squares and metric dimension
摘要
This note addresses the critical issue of paper exclusion. Utilizing several methods, this note shows that using authors only graphs that exclude all papers not only creates a loss of information, but can lead to incorrect interpretation of network structure due to degree projection and because interpretation of vertex degree in the authors only graph is not well defined. Because papers are the products of research groups that are the actual social groups, inclusion of all papers increases the probability of social group duplication. This note utilizes representative papers that reflect distinct research groups. With a departmental collaboration focus, public data for professors from three STEM departments of three U.S. public universities is analyzed to assess the impact of restricting analysis to the authors only graph. Social analysis of the collected data shows a 27% change in the total number of hubs, and different professors identified as hubs, when the authors only graphs are compared to the related bipartite graphs. Because the bipartite authors with distinct research groups graph is the actual social network, metric dimension is used to show that the relative distance structure of the bipartite graph is often defined by the structure of the groups, not that of the authors. These noted changes are primarily due to degree projection during projection graph construction, and are completely independent of data set size. Due to the NP-hard nature of metric dimension, methods that increase computational efficiency for the bipartite authors and groups graph are explored.