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Topic: Biadjacency matrix

	Biadjacency matrix - Wikipedia, the free encyclopedia
		In the special case of a finite, undirected simple bipartite graph, the biadjacency matrix is a (0,1)-matrix.
		The relationship between a bipartite graph and its biadjacency matrix is studied in spectral graph theory.
		The adjacency matrix A for a bipartite graph with a biadjacency matrix B is given by
	en.wikipedia.org /wiki/Biadjacency_matrix (120 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Pisanski University of Ljubljana, Slovenia (Tomaz.Pisanski@fmf.uni-lj.si) The Haar graph H(n) of an integer n is a bipartite graph obtained from a biadjacency matrix B(n) that is a circulant matrix with the first row composed of the binary vector b(n) corresponding to the binary representation of n.
		It turns out that each H(n) is a bipartite Cayley graphs for a dihedral group, although the converse is not true.
		A Haar graph can be viewed as a covering graph of a dipole with voltages taken from a cyclic group.
	www.ijp.si /tomo/work/talks/98/Flagstaff98/sigmac98.txt (186 words)

	[No title]
		A $k\times n$ {\it\lr\/} is a $k\times n$ matrix of entries from $\{1,2,\dots,n\}$ such that no entry is duplicated within any row or any column.
		With $R$ and $G(R)$ we associate $A(R)\in\lnk$ defined by $$\big(A(R)\big)_{ij}=\cases{1,&if $u_i$ is adjacent to $v_j$ in $G(R)$;\cr 0,&otherwise.\cr}$$ We call $A(R)$ the biadjacency matrix of $G(R)$.
		Note that $E(R)$ is the permanent of $\comp{A(R)}$, the biadjacency matrix of $\comp{G(R)}$.
	www.emis.de /journals/EJC/Volume_5/Texfiles/v5i1r11.tex (3783 words)

	Incidence matrix - Definition, explanation
		The incidence matrix is related to the adjacency matrix of its line graph
		The cycle space of a graph is equal to the null space of its incidence matrix.
		In this case the incidence matrix is also a biadjacency matrix of the Levi graph of the structure.
	www.calsky.com /lexikon/en/txt/i/in/incidence_matrix.php (236 words)

	[No title]
		We may also append an extra keyword All to denote that e is all the positions of the adjacency matrix to contain 1.
		Graph[adj, emb] is a simple graph with adjacency matrix adj and embedding emb." GraphComplement::usage = "GraphComplement[g] returns the complement of graph g.
		ToEdges[g, All] returns all the positions in the adjacency matrix that are 1." ToIncidenceMatrix::usage = "ToIncidenceMatrix[g] returns the incidence matrix of graph g.
	abel.math.umu.se /~phl/Mathematica/Basics.m (1557 words)

	Articles - Incidence matrix (Site not responding. Last check: 2007-11-07)
		In mathematics, the incidence matrix of an undirected graph G is a p Ã— q matrix [ b
		The incidence matrix is related to the adjacency matrix of its line graph L (G) by the following theorem:
		The incidence matrix of an incidence structure C is a p Ã— q matrix [ b
	www.advicez.com /articles/Incidence_matrix (210 words)

	ANU - Mathematical Sciences Institute (MSI) - Seminars
		Permanents are matrix functions, similar to determinants,that are useful for solving various combinatorial problems.
		In particular, the permanent of the biadjacency matrix of a bipartite graph will count the number of perfect matchings in the graph.
		In this connection I will demonstrate a graph, first constructed by ANU academic Dr Ian Wanless in 1999, which turns out to be a counterexample to the Holens-Dokovic conjecture on subpermanental ratios.
	www.maths.anu.edu.au /calendar/04.10.16.cal.html (346 words)

	"Glossary of Terms in Combinatorics" (Site not responding. Last check: 2007-11-07)
		Characteristic polynomial \phi - 1) for a graph, the characteristic polynomial of the adjacency matrix (roots are the eigenvalues); 2) for a poset, the generating function of the Möbius function by co-rank
		Eigenvalue - for a graph, an eigenvalue of the adjacency matrix
		Incidence matrix - the matrix in which entry (i,j) is 1 if vertex j belongs to edge i, and 0 if not (for a digraph, 1 if vertex j is the head of edge i, -1 if it is the tail, 0 otherwise)
	www.math.uiuc.edu /~west/openp/gloss.html (11899 words)

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