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Let G be a bipartite graph with μ as an eigenvalue of multiplicity k>1.
If you consider the market of phones to be a bipartite graph (with phones on the left and buyers on the right), at this very moment, many buyers have a strong preference for the new iPhone, and as a result are willing to pay significant amounts of money for it.
Proposition 6 Let G be a bipartite graph.
Let be a bipartite graph with vertices, then (3.3).
Lemma 2.2 Let G = ( U, V ; E ) be a bipartite graph and | U | = m, | V | = n.
Let G= X,Y,E) be a bipartite graph and G′ be the graph obtained from the addition of edges to X in order to obtain a clique.
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The whole system is a bipartite graph.
Note that (M_{U}) is a bipartite graph.
The graph is a bipartite graph with two types of nodes - user nodes and retweet nodes.
Then there exist a spanning subgraph of such that is a bipartite graph and.
Then, by Lemma 3.5, there exist a spanning subgraph such that is a bipartite graph and.
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