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Topic: Adjacency matrix

Related Topics

Adjacency list

Acyclic graph

Diagonal matrix

Spectral graph theory

Incidence matrix

Glossary of graph theory

Graph (mathematics)

Sparse graph

Spanning tree (mathematics)

Identity matrix

Directed acyclic graph

Minimal spanning tree

Tree rotation

Hierarchichal

List of combinatorics topics

	math lessons - List of matrices
		Adjacency matrix - a (0,1)-matrix that is square with all diagonal elements zero.
		Companion matrix - the companion matrix of a polynomial is a special form of matrix, whose eigenvalues are equal to the roots of the polynomial.
		Permutation matrix - matrix representation of a permutation.
	www.mathdaily.com /lessons/List_of_matrices (755 words)

	Adjacency matrix - Wikipedia, the free encyclopedia
		The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
		The adjacency matrix of a complete graph is all 1's except for 0's on the diagonal.
		The adjacency matrix of an undirected graph is symmetric, and therefore has a complete set of real eigenvalues and an orthogonal eigenvector basis.
	en.wikipedia.org /wiki/Adjacency_matrix (947 words)

	Graph Theory Lesson 7
		The adjacency matrix of a graph is an n x n matrix A = (a
		Suppose you are told that the adjacency matrix for a simple graph has 5 rows and 5 columns.
		A graph, its adjacency matrix and the square of its adjacency matrix
	oneweb.utc.edu /~Christopher-Mawata/petersen/lesson7.htm (725 words)

	JoSS: Journal of Social Structure
		Because this approach begins with the raw adjacency matrix and does not deal with expected (based on row and/or column marginals) effects, the results contain a mixture of "signal" and "background" and are thus difficult to interpret.
		matrix (C - E) where E is the matrix of expected values of C, and the eigenvectors are weighted by the reciprocal of the square root of the marginals (Greenacre, 1984; Hoffman and Franke, 1986).
		CONCOR is the iterated calculation of the Pearson correlation of pairs of rows (or columns) of the adjacency matrix.
	www.cmu.edu /joss/content/articles/volume1/RichardsSeary.html (5449 words)

	Trees and their Related Matrix Ranks
		An adjacency matrix of a graph is a {0,1} matrix in which the
		A reduced adjacency matrix for a bipartite graph is a
		is the normal rank of a matrix corresponding to the number of pivots in the matrix.
	www-math.cudenver.edu /~rrosterm/trees/trees.html (1030 words)

	Adjacency Matrices
		Clearly, the number of ones in the adjacency matrix is equal to the number of edges in the graph.
		One advantage of using an adjacency matrix is that it is easy to determine the sets of edges emanating from a given vertex.
		In this case, there are twice as many ones in the adjacency matrix as there are edges in the undirected graph.
	www.brpreiss.com /books/opus6/html/page532.html (316 words)

	Introduction to Graph Theory
		Adjacency matrix M is a V matrix, where the dimensions represent vertices (numbered in some arbitrary manner), and the elements are
		The size of the adjacency matrix is always V, regardless of the size of E.
		Adjacency lists are scanned only when the vertex is dequeued, thus each adjacency list is scanned exactly once.
	www.owlnet.rice.edu /~comp314/lec/week2/GraphIntro.htm (1321 words)

	[No title]
		adjacency matrix: A network (graph) may be represented by a matrix of zeros and ones, with a one indicating that two nodes are connected (adjacent), and a zero otherwise.
		Adjacency spectrum: The adjacency matrix of a graph, like any matrix, may be subject to an eigen decomposition.
		Sparse matrix techniques are those which avoid any manipulation of the matrix that would affect the sparseness property (e.g., taking the inverse will generally do this, as will correlating each row or column with all the others).
	www.insna.org /FAQ/Glossaries/Seary.Richards.html (1697 words)

	Adjacency matrix
		This is referred to as an adjacency matrix representation.
		numerical matrix, or by having a matrix of pairs of booleans and numbers or, possibly, by collapsing the representation into a single matrix by using a device such as indicating non-existence of paths by ``infinite'' weights.
		Secondly the adjacency matrix representation, in its simple form, is unable to represent graphs in which there may be more than one arc between some nodes.
	www.cogs.susx.ac.uk /courses/dats/notes/html/node132.html (245 words)

	Graphs Glossary (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-09)
		A 1 in the ij-th position of the matrix means that there is an edge (or arc) from vertex i to vertex j.
		A 0-1 matrix whose rows are indexed by the vertices of a graph and whose columns are indexed by the edges.
		A 1 in the ij-th position of the matrix means that the vertex i is on the edge j.
	www-math.cudenver.edu.cob-web.org:8888 /~wcherowi/courses/m4408/glossary.htm (1926 words)

	Adjacency matrix (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-09)
		The relationship between a graph and its Adjacency matrix is studied in spectral graph theory.
		The Adjacency matrix of an undirected graph is symmetric, and therefore has a complete set of eigenvalues and orthogonal eigenvector basis.
		Given the two Adjacency matrices, it is possible to reconstruct the permutation matrix used: see Permutation matrixSolving for P. Note, however, that the converse is not true: two graphs may posses the same set of eigenvalues but not be isomorphic (one cannot hear the shape of a graph).
	adjacency-matrix.iqnaut.net.cob-web.org:8888 (735 words)

	Calculation of source counts from Time Directed Partner Graphs:
		When using adjacency matrices the source count of a node is the number of distinct nodes that can reach the node of interest.
		The adjacency matrices are a convenient representation of TDPG but have the disadvantage that they can be unwieldy in terms of both the matrix algebra involved in the calculation of measures and the space required to represent TDPG's.
		When a relationship is initiated either a node will be added to an adjacency matrix representing a connected component of the TDPG or two adjacency matrices will be joined to form a single adjacency matrix which represents the connected component formed by the connection of two previously unconnected components.
	www-personal.umich.edu /~criolo/matrix/Calculation.html (1349 words)

	Matrix theory - Wikipedia, the free encyclopedia
		Matrix theory is a branch of mathematics which focuses on the study of matrices.
		Therefore matrix theory is usually considered as a branch of linear algebra.
		A permutation matrix is the matrix representation of a permutation; it is a square matrix with entries 0 and 1, with just one entry 1 in each row and each column.
	en.wikipedia.org /wiki/Matrix_theory (287 words)

	Graphs
		An adjacency matrix is easily implemented as an array.
		The adjacency matrix of a weighted graph can be used to store the weights of the edges.
		A weighted adjacency matrix is easily defined in any imperative programming language.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Graph (1162 words)

	NSDL Metadata Record -- Adjacency Matrix -- from MathWorld
		The adjacency matrix of a simple graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in position (v_i, v_j) according to whether v_i and v_j are adjacent or not.
		For a simple graph with no self-loops, the adjacency matrix must have 0s on the diagonal.
		For an undirected graph, the adjacency matrix is symmetric.
	nsdl.org /mr/697188 (124 words)

	Adjacency Matrix (Site not responding. Last check: 2007-10-09)
		I find Gnosticism interesting because it has managed to survive all these years despite losing its status as a mainstream religion, and because it illustrates some of the diverse religious thought that competed for the souls of early Christians.
		Of course, Bassey did not have a track on the Matrix soundtrack, but the Propellerheads did -- in fact, the use of their tune "Spybreak!" during the movie's climactic hotel-scene battle both heightened the excitement of the movie and made the Propellerheads quite famous.
		Just like the citizens of The Matrix, we are mostly oblivious to reality, in part because somebody has convinced us that consuming entertainment is a worthwhile pursuit.
	www.erin.utoronto.ca /~pnijjar/ritual/matrix.html (1998 words)

	How to Input a Graph on a Computer? (Site not responding. Last check: 2007-10-09)
		Consider a block of numbers, called a matrix, with p rows, representing the p vertices in order, and p columns, representing the same p vertices in order.
		When you input this adjacency matrix into the text area, do not include the vertex names, only input the numbers.
		the adjacency matrix, in general, is not symmetric for a directed graph.
	www.uwstout.edu /faculty/wuming/Samples/AdjacencyMatrix.html (323 words)

	Graph Data Structures
		Adjacency matrices win for algorithms that repeatedly ask, ``Is (i,j) in G?'' However, most graph algorithms can be modified to eliminate such queries.
		An elementary implementation of a ``lazy'' adjacency matrix in Pascal, which does not have to be initialized, appears in [MS91].
		The basic adjacency list and matrix data structures are presented in essentially all books on algorithms or data structures, including [CLR90, AHU83, Tar83].
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK3/NODE132.HTM (1450 words)

	Adjacency list - Wikipedia, the free encyclopedia
		One difficulty with the adjacency list structure is that it has no obvious place to store data associated with the edges of a graph, such as the lengths or costs of the edges.
		For a graph with a sparse adjacency matrix an adjacency list representation of the graph occupies less space, because it does not use any space to represent edges which are not present.
		Using a naive array implementation of adjacency lists on a 32-bit computer, an adjacency list for an undirected graph requires about 8e bytes of storage, where e is the number of edges: each edge gives rise to entries in the two adjacency lists and uses four bytes in each.
	en.wikipedia.org /wiki/Adjacency_list (637 words)

	Linear Algebra Glossary (Site not responding. Last check: 2007-10-09)
		Thus, an adjacency matrix is a zero-one matrix.
		The inverse of a (nonsingular) circulant matrix is a circulant matrix.
		The transpose of a circulant matrix is a circulant matrix.
	www.csit.fsu.edu /~burkardt/papers/linear_glossary.html (13553 words)

	adjacency-matrix representation (Site not responding. Last check: 2007-10-09)
		Definition: A representation of a directed graph with n vertices using an n × n matrix, where the entry at (i,j) is 1 if there is an edge from vertex i to vertex j; otherwise the entry is 0.
		A weighted graph may be represented using the weight as the entry.
		An undirected graph may be represented using the same entry in both (i,j) and (j,i) or using an upper triangular matrix.
	www.nist.gov /dads/HTML/adjacencyMatrixRep.html (168 words)

	Spectra of random graphs with given expected degrees -- Chung et al. 100 (11): 6313 -- Proceedings of the National ...
		the spectrum of the adjacency matrix of a power-law graph obeys
		and the eigenvalues of the adjacency matrices are plotted,
		Eigenvalues of the Adjacency Matrix of Power-Law Graphs
	www.pnas.org /cgi/content/full/100/11/6313 (2365 words)

	NetUtils
		reterns a new matrix which is the reverse similarity->disimilairty, disimilarity->similart of the passed matrix.
		returns a matrix which is the symetrized (i->j and j->i = Max((i->j,j->i))) version of the passed adjacency matrix.
		returns a matrix in which each value is equal to the original subtracted from the max+min values of the original.
	www.stanford.edu /group/sonia/doc/sonia/NetUtils.html (491 words)

	Michael Nielsen » Blog Archive » Expander graphs III: graphs and their adjacency matrices
		By describing a graph in terms of matrices we enable all the powerful tools of linear algebra to be brought to bear on graph theory, and we’ll see that there are all sorts of interesting connections between graphs and linear algebraic concepts such as eigenvalues.
		Note that the adjacency matrix may be considered as a matrix over any field, and the result of the exercise is true over any field.
		But besided adjacency matrix graphs are characterized by laplasian, matrixes given in a cut and flow space.
	www.qinfo.org /people/nielsen/blog/?p=220 (2288 words)

	[No title]
		ADJACENCY MATRIX is a symmetric square matrix whose entries are 0 or 1 and whose diagonal elements are all 0.
		The first step is to 'mark' all the nodes that have an edge between them and the node i (this is what the adjacency matrix is for).
		If node j is not among the 'marked' nodes then you should repeat this operation for all nodes you've 'marked' so far and find all the nodes that have edges with those that are now 'marked' and so on.
	www.cs.bgu.ac.il /~clang051/assignments/assignment2/work2.doc (536 words)

	CS136, Lecture 28
		In an adjacency matrix we fill in the entries with values giving information about the existence or non-existence of edges.
		An adjacency list is composed of a list of nodes or vertices.
		Adding edges is relatively straightforward: just add it in the adjacency lists of vertices if it is not already there.
	www.cs.williams.edu /~kim/cs136/s98/Lectures/Lec28.html (816 words)

	Class notes CS251B -- Winter 1997
		One might grab all the bits from the adjacency matrix and concatenate them to form a binary string.
		One may improve on this scheme in two ways: the initial string obtained from the adjacency matrix may be compressed by standars compression methods.
		The matrix for this graph would contain all 1's therefore there would be no point in storing it.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic25 (1667 words)

	Analyses supported by IAN (as of October 7th, 2004)
		Note: This measure is derived from an adjacency matrix.
		Definition: given an adjacency matrix between the classes present ASM = the sum of the squared adjacencies for all combinations of the classes present.
		First the main diagonal of the adjacency matrix is set to zero and the matrix is rescaled to sum to 1.0.
	landscape.forest.wisc.edu /projects/ian/analyses.htm (2567 words)

	Boost Graph Library: Adjacency Matrix
		Figure 1 shows the adjacency matrix representation of a graph.
		The advantage of this matrix format over the adjacency list is that edge insertion and removal is constant time.
		Figure 2 shows an adjacency matrix representation of an undirected graph.
	cs.brown.edu /people/jwicks/boost/libs/graph/doc/adjacency_matrix.html (856 words)

	Adjacency Matrix (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-09)
		For adjacency matrix representation of a graph G = (V, E) we assume that the vertices are numbered 1,2.
		This representation of a graph G then consist of a V matrix A = [aij } such that:
		Note : Sum of rows of adjacency matrix is the degree of vertices.
	engr.smu.edu.cob-web.org:8888 /cse/3353/graphs2/tsld005.htm (50 words)

	Graph algorithms
		There are two standard ways to represent a graph G=(V,E): as a collection of adjacency lists or as an adjacency matrix.
		Like the adjacency list representation adjacency matrix representation can be used for weighted graphs.
		Although the adjacency-list representation is asymptotically at least as efficient as the adjacency-matrix representation, the simplicity of the latter may make it preferable when graphs are reasonably small.
	members.fortunecity.com /vidit/ega.html (267 words)

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