The Matrix-Forest Theorem and Measuring Relations in Small Social Groups
<|reference_start|>The Matrix-Forest Theorem and Measuring Relations in Small Social Groups: We propose a family of graph structural indices related to the Matrix-forest theorem. The properties of the basic index that expresses the mutual connectivity of two vertices are studied in detail. The derivative indices that measure "dissociation," "solitariness," and "provinciality" of vertices are also considered. A nonstandard metric on the set of vertices is introduced, which is determined by their connectivity. The application of these indices in sociometry is discussed.<|reference_end|>
@article{chebotarev2006the,
    title={The Matrix-Forest Theorem and Measuring Relations in Small Social Groups},
    author={Pavel Chebotarev and Elena Shamis},
    journal={Automation and Remote Control 58 (1997) No. 9 1505-1514},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0602070},
    primaryClass={math.CO cs.IR math.AG}
}