Spectral gap in random bipartite biregular graphs and applications
Keyword(s):
Abstract We prove an analogue of Alon’s spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara–Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A by-product of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.
2006 ◽
Vol 27
(4)
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pp. 1056-1066
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Keyword(s):
1998 ◽
Vol 12
(02)
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pp. 191-205
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1998 ◽
Vol 66
(4)
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pp. 261-272
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Keyword(s):
2002 ◽
Vol 185
◽
pp. 234-235