科研之友
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摘要
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or -1, and each adjacency is signed the negative of the product of the incidences. An oriented hypergraph is balanced if the product of the adjacencies in each circle is positive. We provide a combinatorial interpretation for entries of kth power of the oriented hypergraphic Laplacian via the number of signed weak walks of length k. Using closed weak walks we prove a new characterization of balance for oriented hypergraphs and matrices that generalizes Harary's Theorem for signed graphs.
- 出版日期2015-11-15
