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Topic: Adjacency list

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Adjacency matrix

Glossary of graph theory

Connected graph

Spanning tree (mathematics)

List of graph theory topics

Incidence matrix

Directed acyclic graph

Sparse graph

Minimal spanning tree

Tree rotation

Measurable function

RSA

Edge

Metric space

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	Adjacency list - Wikipedia, the free encyclopedia
		In graph theory, an adjacency list is the representation of all edges or arcs in a graph as a list.
		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 linked list implementation on a 32-bit computer, an adjacency list for an undirected graph requires about 16e bytes of storage, where e is the number of edges.
	www.wikipedia.org /wiki/Adjacency_list (426 words)

	Adjacency matrix - Wikipedia, the free encyclopedia
		For sparse graphs, that is graphs with few edges, an adjacency list is often the preferred representation because it uses less space.
		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.
	en.wikipedia.org /wiki/Modified_adjacency_matrix (812 words)

	Adjacency list -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		In (additional info and facts about graph theory) graph theory, an adjacency list is the representation of all edges or arcs in a (A drawing illustrating the relations between certain quantities plotted with reference to a set of axes) graph as a list.
		In (The branch of engineering science that studies (with the aid of computers) computable processes and structures) computer science, an adjacency list is a closely related ((computer science) the organization of data (and its storage allocations in a computer)) data structure for representing graphs.
		For a graph with a (additional info and facts about sparse) 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.
	www.absoluteastronomy.com /encyclopedia/a/ad/adjacency_list.htm (500 words)

	adjacency-list representation (Site not responding. Last check: 2007-11-07)
		Definition: A representation of a directed graph with n vertices using an array of n lists of vertices.
		List i contains vertex j if there is an edge from vertex i to vertex j.
		An undirected graph may be represented by having vertex j in the list for vertex i and vertex i in the list for vertex j.
	www.nist.gov /dads/HTML/adjacencyListRep.html (180 words)

	McGill University School of Computer Science: CS203A
		a list of courses that must be taken and passed before the student may register for the course.
		List the order in which the vertices would be visited in a DFS traversal starting at vertex m.
		Adjacency list representations are just like hashtables that use chaining (see lectures notes).
	cgm.cs.mcgill.ca /~msuder/courses/203/assignments/4/solutions (1059 words)

	CS141 Lab 1 (Site not responding. Last check: 2007-11-07)
		The sum of lenghts of all the adjacency lists for an undirected graph is 2E, since for every edge (a,b), there will be a list element “b” on the a’s list and a list element “a” on the b’s list.
		The sum of lenghts of all the adjacency lists for a directed graph is E, since for every edge(a,b), there will only be a list element “b” on the a’s list.
		Weigthed graphs are easy to represent with adjacency lists: if the weight of the edge (a,b) is W, just store W along with the “b” element on the a’s list.
	www.cs.ucr.edu /cs141/cs141_03spr/lab6.html (1010 words)

	Graph Representations and Traversals
		A very common representation of graphs is the adjacency list, which consists of an array of vertices, each of which contains a list of all adjacent vertices (in an arbitrary order).
		An advantage of the adjacency list representation is that it easily can be extended to support variants of graphs.
		Both the adjacency list and the adjacency matrix are vertex-centric representations.
	www.cs.cornell.edu /courses/cs312/2003sp/lectures/rec19.html (776 words)

	Prolog Tutorial -- 2.9 (Site not responding. Last check: 2007-11-07)
		Notice that an adjacency list can be used to define the map as long as every region is adjacent to at least one other region (not disconnected regions).
		Now, given the adjacency list and a list of colors, one should be able to compute proper colorings -- that is, colorings where adjacent regions have different colors.
		In words, stated in a top-down fashion, the intention is to color the map by means of first calculating the regions from the adjacency list, then color the map, then check to see that the coloring is not in conflict.
	www.csupomona.edu /~jrfisher/www/prolog_tutorial/2_9.html (409 words)

	CS312 Lecture 14: Graph Representations. Graph Traversals
		Adjacency lists can be used to represent both directed and undirected graphs.
		Adding new vertices to the front of the list assures that the children of the current node are processed before its siblings.
		The equivalence is predicated upon listing the children of nodes in the tree in the "right" order in the adjacency lists: left child first, followed by the right child.
	www.cs.cornell.edu /courses/cs312/2004fa/lectures/lecture14.htm (2563 words)

	Data Structures for Graphs (Site not responding. Last check: 2007-11-07)
		Adjacency matrices are the simplest way to represent graphs.
		An adjacency list consists of an n-element array of pointers, where the ith element points to a linked list of the edges incident on vertex i.
		Also, depending upon the operations you will perform on each list, you may or may not want it to be doubly linked, so that you can move backwards as easily as you move forwards.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK2/NODE61.HTM (501 words)

	Dijkstra's algorithm - Wikipedia, the free encyclopedia
		Now sequence S is the list of vertices on the shortest path from s to t.
		edges, Dijkstra's algorithm can be implemented more efficiently by storing the graph in the form of adjacency lists and using a binary heap or Fibonacci heap as a priority queue to implement the Extract-Min function.
		To obtain a ranked list of less-than-optimal solutions, the optimal solution is first calculated.
	www.wikipedia.com /wiki/Dijkstras_Algorithm (1082 words)

	Graph Definitions
		An adjacency matrix is a two dimensional array whose dimensions are equal to the number of vertices.
		An adjacency list is a list of vertices to which a vertex has connections (i.e., it is a list of vertices that are attached to this vertex by edges).
		As a rough rule of thumb, matrices are typically used for dense arrays and adjacency lists for sparse arrays.
	www.cs.utk.edu /~parker/Courses/CS302-fall03/Notes/graph-defs.html (1629 words)

	Measuring Algorithm Efficiency
		Then apply your algorithm to convert the binary search tree to a doubly linked list, showing the status of the conversion at each node of the search as it is consumed and moved into the doubly linked list.
		Let the adjacency list representation of a graph (0, 1 symmetric matrix) be given by a packed edge list.
		Describe an algorithm for reordering the edge list in place so all adjacency lists follow a new vertex ordering given by a permutation p(1), p(2),..., p(n).
	engr.smu.edu /cse/7350/7350-f99hw2.html (589 words)

	Intro to Algorithms: CHAPTER 23: ELEMENTARY GRAPH ALGORITHMS
		Adjacency lists can readily be adapted to represent weighted graphs, that is, graphs for which each edge has an associated weight, typically given by a weight function w : E
		Figures 23.1(c) and 23.2(c) are the adjacency matrices of the undirected and directed graphs in Figures 23.1(a) and 23.2(a), respectively.
		Because the adjacency list of each vertex is scanned only when the vertex is dequeued, the adjacency list of each vertex is scanned at most once.
	www.personal.kent.edu /~mlu3/CSCourses/AdvAlgorithms/CLR-BOOK/books/book6/chap23.htm (10001 words)

	[No title]
		As far as their difference is concerned we would like to enhance the list of objects being returned, by some entity that will encapsulate in total component ASSOCIATED PRESENTATION OF EXAMPLES Component SUPERCLASS collects in a list all the vertices that represent super- classes of a given vertex v.
		The list of the immediate superclasses is created by traversing the graph and by checking for every vertex whether the given vertex v is a member of their list of A-kind neighbors.
		The call is propagated along the Adjacencies of the graph, collecting in the empty Vertex_List all the C-kind vertices that are alternation reachable by v.
	www.ccs.neu.edu /research/demeter/papers/derived-edges/more-history/component-reuse-mechanism/from-irini (1485 words)

	Part 5: From Trees to Graphs
		For example, in adjacency list representation (b) in Figure 4, the node a has b in its adjacency list, and node b also has node a in its adjacency list.
		Therefore, an adjacency list is a very space-efficient representation of a graph.
		Recall that with the adjacency list approach, if there exists an undirected edge between nodes u and v, then u will have a reference to v in its adjacency list and v will have a reference to u in its adjacency list.
	msdn.microsoft.com /library/en-us/dv_vstechart/html/datastructures_guide5.asp?frame=true (5113 words)

	Graphs
		Associated with each vertex is its adjacency list: this is a list of the names of its immediate neighbors.
		Adjacency matrix is more efficient if the graph is dense; adjacency list is more efficient if the graph is sparse.
		To speed things up (if the word list is very large), don't write a nested loop to try all pairs of words to see if they are adjacent.
	www.cs.princeton.edu /introcs/48graph (2092 words)

	Adjacency List
		The only data structure actually have to implement for project 1 is and adjacency list.
		You'll recall that an adjacency is conceptually a 'list of lists', ie:
		Note that insertion/deletion from this structure is O(log(n)log(m)), where n is the number of nodes in the graph and m is the degree of the graph (the max number of edges incident to a single vertex).
	www.cs.umd.edu /class/sum2003/cmsc420/sum3v101/node8.html (931 words)

	CS 136, Lecture 30
		An adjacency list is composed of a list of nodes or vertices.
		Similarly the list of edges could be any kind of collection (class containing add, remove, contains, and elements) including all kinds of lists and binary search tree.
		Adding edges is relatively straightforward: just add it in the adjacency lists of vertices if it is not already there.
	www.cs.williams.edu /~andrea/cs136/Lectures/Lec30/Lec30.html (359 words)

	Graph Searching
		The implementation appears to be dependent on whether the edge list is implemented as a list or a matrix.
		Adjacency matrix: The iterator for an adjacency matrix needs to iterate through the vertex's row in the matrix and return edges as they are found.
		Note that the iterator for the adjacency list simply uses the dList's interface for moving through the list.
	www.cs.utk.edu /~bvz/cs302/notes/graph-searching.html (579 words)

	Graph representation
		Two common ways to represent graphs on a computer are as an adjacency list or as an adjacency matrix.
		Corresponding to each vertex is a list (either an array or linked list) of its neighbours.
		with an adjacency list might require, say, 10,000 words for the node plus 20,000 words for the list of neighbours: 30,000 words or 120K.
	www.cs.toronto.edu /~heap/270F02/node35.html (201 words)

	TRIANGULATE
		TRIANGULATE can, optionally, return the adjacency list that describes, for each node, the adjacent nodes in the Delaunay triangulation.
		With this list, the Voronoi polygon (the polygon described by the set of points which are closer to that node than to any other node) can be computed for each node.
		The adjacency list is ordered in the counter-clockwise direction.
	www.astro.virginia.edu /class/oconnell/astr511/IDLresources/idl_5.1_html/idl1e0.htm (700 words)

	Databases: Adjacency List or Nested Sets?
		I tend to think about nested sets as an extention of an adjacency list, were you do a little more bookkeeping work to maintain your lft and rgt indexes but you get the added benefit of being able to easily select all of the children of specific node with a simple select statement.
		As the previous poster suggests, you can model your Departments table as an Adjacency list (or extend that to a nested sets approach) and the Employees table is trivial, then your table of Employee-Deptartment would just list the departments that any employee may belong to.
		With the Adjacency list approach, you'd have to do a bunch of querys to pull out all the children of the manager at level 3, then level 4....
	www.experts-exchange.com /Databases/Q_21517934.html (541 words)

	CMPS 101
		The purpose of this assignment is to understand and implement a graph ADT and associated algorithms.
		The adjacency list representation of a graph consists of a sequence of lists, one for each vertex in the graph, where each list gives the neighbors of the corresponding vertex.
		After these lines are read your program will print out the adjacency list representation of the graph.
	www.cse.ucsc.edu /classes/cmps101/Winter00/pa3.html (1087 words)

	Using the Boost Graph Library
		is because the vertex descriptors (which in this case are indices that correspond to the vertices' place in the vertex list) must be adjusted in the out-edges for the whole graph.
		The former is easier to use and requires less effort, whereas the latter is compatible with older, broken compilers and is backward-compatible with Boost versions prior to 1.32.0.
		One may specify internal properties via property lists, which are build from instances of the property class declared as follows.
	www.boost.org /libs/graph/doc/using_adjacency_list.html (1960 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Partial Key to HW 4 \large{\bf {4-1.} (10)} \begin {description} \item [a.] Go through the adjacency matrix M, for each M[i,j]=1, add j to i's adjacency list.
		Then, go through the adjacency list for each vertex i, if j is in the adjacency list of i, and i>j, set $M[i, k]=1$, $M[j, k]=1$, and $k+=1$.
		\item [c.] Go through each column of the adjacency list, find i, j such that $M[i, k]=0$ and $M[j, k] =0$, the add i to j's adjacency list and j to i's adjacency list.
	www.cs.sunysb.edu /~skiena/373/hw/key4.txt (811 words)

	Class notes CS251B -- Winter 1997
		One may improve on this scheme in two ways: the initial string obtained from the adjacency matrix may be compressed by standars compression methods.
		It is exactly like hashing with chaining where we have a list (array) of vertices, each of which stores a linked list of all of its neighbors.
		The Adjacency List shows, for each node, a list of the other nodes to which it is connected.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic25 (1667 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The running time is given by the length of the list, i.e.
		The total number of vertices in adjacency list equals the number of edges, so the running time is O(E).
		Give and adjacency list representation for a complete binary tree on 7 vertices.
	longwood.cs.ucf.edu /courses/cop3503/spring04/recit/week9_key.doc (288 words)

	[No title]
		For the adjacency matrix representation, you will use Floyd's algorithm (described in Section 9.9) to compute all-pairs shortest distances.
		Add C code to the file shortest-list.c to output ONE shortest path using the adjacency list representation.
		That function gets an adjacency matrix as one of its parameters and YOU must convert the adjacency matrix into an adjacency list representation BEFORE computing the shortest path.
	www.dgp.toronto.edu /people/JamesStewart/270/9697f/hwk2/hwk2.txt (1187 words)

	Spanning Trees
		At this point, back up to the adjacency list of the last vertex (on the stack).
		The only vertex on six s adjacency list is four which was visited so four is popped from the stack
		The only vertex on five's list is four which was previously visited.
	www.iwu.edu /~sander/CS255/Notes/SpanningTrees.html (886 words)

	C++ Code Documentation \| geom::surface0::Boundary
		(i,j) represents an edge, and F = {f0,f1,...} a list of faces adjacent to the edge.
		_adjacency_list[i] is a list of the vertices adjacent to i compute_edge() Compute a list of edges and the faces they bound.
		compute an associative array of edges, together with a list of the faces of which they are edges algorithm: cycle through all the faces, making a hash of all edges every time an edge occurs in a face, increment a counter.
	www.gang.umass.edu /software/code/doc116.html (216 words)

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