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1 Connectivity (graph theory) - Wikipedia
https://en.wikipedia.org/wiki/Connectivity_(graph_theory)
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) ...
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2 Connectivity in a directed graph - Tutorialspoint
https://www.tutorialspoint.com/Connectivity-in-a-directed-graph
To check connectivity of a graph, we will try to traverse all nodes using any traversal algorithm. After completing the traversal, ...
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3 Check if a directed graph is connected or not - GeeksforGeeks
https://www.geeksforgeeks.org/check-if-a-directed-graph-is-connected-or-not/
Check if a directed graph is connected or not · Take two bool arrays vis1 and vis2 of size N (number of nodes of a graph) and keep false in all ...
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4 Graph connectivity - AlgoWiki
https://algowiki-project.org/en/Graph_connectivity
The edge connectivity of a graph can be found by using Gabow's algorithm The time complexity is O(k m \ln (n^2/m)) for directed graphs and O(m + ...
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5 Graph connectivity
https://web.mat.bham.ac.uk/R.W.Kaye/numerics/graphcon1.html
The function randomdigraph randomly generates a digraph with a certain probability of an edge, and randomsimplegraph creates a "random" graph for testing, which ...
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6 Connectivity related functions - Graph Theory
https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/connectivity.html
Check whether the (di)graph is connected. connected_components(). Return the list of connected components. connected_components_number().
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7 4 Ways to Check if a Graph is Fully Connected - Noveltech
https://www.noveltech.dev/fully-connected-graph/
› fully-connected-graph
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8 C Program to Check the Connectivity of Graph Using DFS
https://www.sanfoundry.com/c-program-check-connectivity-graph-dfs/
C Program to Check the Connectivity of Graph Using DFS · #include<stdio.h> · #include<conio.h> · int a[20][20], reach[20], n; · void dfs(int v) { · int i; · reach[v] ...
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9 How do I find if undirected graph is connected or not using DFS?
https://www.quora.com/How-do-I-find-if-undirected-graph-is-connected-or-not-using-DFS
DFS is an algorithm to traverse a graph, meaning it goes to all the nodes in the same connected component as the starting node. If we traverse the graph ...
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10 A Simple Test on 2-Vertex- and 2-Edge-Connectivity - arXiv
https://arxiv.org/pdf/1209.0700
The algorithm computes all bridges and cut vertices of the input graph in the same time. 1 Introduction. Testing a graph on 2-connectivity (i.e., 2-vertex- ...
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11 INSTITUT F¨UR INFORMATIK Graph Connectivity - mediaTUM
http://mediatum.ub.tum.de/doc/1094497/TUM-I0422.pdf
check k-vertex (k-edge) connectivity,. • compute the vertex (edge) connectivity, and. • compute the maximal k-connected components of a given graph.
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12 Connectivity Algorithms - Computer Science and Engineering
https://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
Even, Graph Algorithms, Computer Science, 1979. 6. S. Even and R. E. Tarjan, “Network flow and testing graph connectivity,”. SIAM Journal of Computing 4 (1975) ...
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13 Connected graph components - MATLAB conncomp
https://www.mathworks.com/help/matlab/ref/graph.conncomp.html
If G is a directed graph, then two nodes belong to the same strong component only if there is a path connecting them in both directions. example. bins = ...
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14 Graph Components and Connectivity
https://reference.wolfram.com/language/guide/GraphComponents.html
A graph may not be fully connected. For instance, only about 25% of the web graph is estimated to be in the largest strongly connected component.
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15 Find the connectivity of directed and undirected graphs - GitHub
https://github.com/adriankato/Graph_Connectivity
To create a program that checks the connectivity of an undirected or directed graph by analyzing the adjacency matrix given by the user.
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16 Connectivity and other graph properties - LEMON
http://lemon.cs.elte.hu/pub/doc/latest-svn/a00850.html
Check that the given directed graph is strongly connected. The graph is strongly connected when any two nodes of the graph are connected with directed paths in ...
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17 Edge connectivity / Vertex connectivity - CP-Algorithms
https://cp-algorithms.com/graph/edge_vertex_connectivity.html
For example an already disconnected graph has the vertex connectivity 0 <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> $0$ , ...
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18 Connected Components in a Graph - Baeldung
https://www.baeldung.com/cs/graph-connected-components
Moreover, if there is more than one connected component for a given graph then the union of connected components will give the set of all ...
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19 Connectivity — NetworkX 2.8.8 documentation
https://networkx.org/documentation/stable/reference/algorithms/connectivity.html
Tests to see if an edge in a graph is locally k-edge-connected. K-edge-components#. Algorithms for finding k-edge-connected components and subgraphs. A k ...
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20 How to check whether a graph is connected in polynomial time?
https://cs.stackexchange.com/questions/11177/how-to-check-whether-a-graph-is-connected-in-polynomial-time
Make a BFS/DFS traversal on the graph. If you visited every vertex then it is connected otherwise ...
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21 ConnectivityInspector (JGraphT : a free Java graph library)
https://jgrapht.org/javadoc/org.jgrapht.core/org/jgrapht/alg/connectivity/ConnectivityInspector.html
Allows obtaining various connectivity aspects of a graph. The inspected graph is specified at construction ... Test if the inspected graph is connected.
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22 5.7 Connectivity
https://www.whitman.edu/mathematics/cgt_online/book/section05.07.html
If it is possible to disconnect a graph by removing a single vertex, called a cutpoint, we say the graph has connectivity 1. If this is not possible, ...
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23 Discrete Mathematics II (Spring 2015) - 10.4 Connectivity
http://courses.ics.hawaii.edu/ReviewICS241/morea/graphs/Graphs4-QA.pdf
Let n be a nonnegative integer and G an undirected graph. A path of length n from u to v in G is a sequence of n edges e1,...,en of G for which ...
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24 Property Testing in Sparse Directed Graphs - Springer Link
https://link.springer.com/chapter/10.1007/978-3-642-33090-2_52
As our first main result, we we present the first property testing algorithm for strong connectivity in this model, having a query complexity of \ensuremath{\ ...
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25 Connectivity related functions — Sage 9.3.beta9 Reference ...
http://sporadic.stanford.edu/reference/graphs/sage/graphs/connectivity.html
Check whether the (di)graph is connected. connected_components(). Return the list of connected components. connected_components_number().
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26 Graph Connectivity With Threshold - LeetCode
https://leetcode.com/problems/graph-connectivity-with-threshold/
› problems › graph-connectivity-w...
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27 Data.Graph.Connectivity - Hackage
https://hackage.haskell.org/package/graphite/docs/Data-Graph-Connectivity.html
Tell if two vertices of a graph are connected. Two vertices are connected if it exists a path between them. The order of the vertices is relevant when the ...
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28 edge_connectivity: Edge connectivity. in igraph - Rdrr.io
https://rdrr.io/cran/igraph/man/edge_connectivity.html
Logical constant. Whether to check that the graph is connected and also the degree of the vertices. If the graph is not (strongly) connected then the ...
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29 Connectivity | Graph Analysis | yFiles for HTML Documentation
https://docs.yworks.com/yfiles-html/dguide/analysis/analysis-connectivity.html
They offer services to check if a graph is connected, strongly connected or even biconnected or how the nodes could be distributed to two or more partitions ...
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30 An Algorithm for Determining Whether the ... - SIAM Journals
https://epubs.siam.org/doi/pdf/10.1137/0204034
SHIMON EVEN. Abstract. The algorithm presented in this paper is for testing whether the connectivity of a large graph ofn vertices is at least k.
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31 IMPROVED ALGORITHMS FOR GRAPH FOUR
https://www.cs.utexas.edu/~vlr/papers/fourcon.pdf
The other uses the O(m) algorithm for testing triconnectivity [HoTa, MiRa2] to test four- connectivity in a triconnected graph in O(mn) time by deleting ...
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32 2-Connectivity in Directed Graphs - DROPS
https://drops.dagstuhl.de/opus/volltexte/2016/6345/pdf/LIPIcs-ESA-2016-1.pdf
and vertex connectivity are fundamental concepts in graph theory with numerous ... However, this can be easily checked in linear time, yielding the ...
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33 Graphs, Connectivity, and Traversals
https://home.csulb.edu/~tebert/teaching/lectures/328/graphs/graphs.pdf
The following proposition suggests a way to efficiently check if a directed graph is a DAG. Theorem 4. If directed graph G = (V,E) is a DAG, then it must have ...
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34 Fast parallel algorithms for testing k-connectivity of directed ...
https://users.cecs.anu.edu.au/~bdm/papers/kconn.pdf
It appears that no NC algorithms have previ- ously appeared for testing a directed graph for k-edge connectivity or k-vertex connectivity, even.
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35 c# - How to check simple connectivity in graph? - Stack Overflow
https://stackoverflow.com/questions/40833722/how-to-check-simple-connectivity-in-graph
From my understanding you're looking for a whole row of 0 and a whole column of 0. If you spot either then return false. Roughly something like this: ...
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36 Solved 5. Consider the following algorithm to check | Chegg.com
https://www.chegg.com/homework-help/questions-and-answers/5-consider-following-algorithm-check-connectivity-graph-defined-adjacency-matrix-algorithm-q26399885
5. Consider the following algorithm to check connectivity of a graph defined by its adjacency. Show transcribed image text. Expert Answer.
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37 The Complexity of Graph Connectivity
https://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/AVI/PRAGUE/conn.pdf
the graph connectivity problem in several computational models, ... It has proven a fertile test case for comparing basic resources,.
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38 3 Dynamic Algorithms for Graph Connectivity
http://www.cs.cmu.edu/~15850/notes/lec3.pdf
The dynamic graph connectivity problem has been studied along all of these axes, which makes it exhausting to give ... When a new edge is added, we check if.
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39 Graph Algorithms
https://math.hws.edu/eck/cs327_s04/chapter9.pdf
Kruskal's algorithm is simple in concept, but we still need a procedure for checking whether adding an edge will introduce a cycle. One way to do this would be ...
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40 Connectivity check in 3-connected planar graphs with obstacles
https://www.sciencedirect.com/science/article/pii/S157106530800084X
We define a vertex labelling for every planar 3-connected graph with n vertices from which one can answer connectivity queries.
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41 Connectivity and Paths
https://www.cs.sfu.ca/~ggbaker/zju/math/paths.html
An undirected graph is called connected if there is a path between every pair of nodes in the graph. So obviously, unconnected graphs are ones where there are ...
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42 Chapter 5 Connectivity in graphs
https://www.csd.uoc.gr/~hy583/papers/ch17.pdf
This chapter references to graph connectivity and the algorithms used to distinguish ... We can design an algorithm to check these conditions.
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43 A Study of Connectivity on Dynamic Graphs: Computing ...
https://hal.archives-ouvertes.fr/hal-02473325/document
The problem of graph connectivity is relevant to many applications ... Algorithms 4 and 5 to check if one component p1 dominates another component.
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44 [PDF] Graph Connectivity - Semantic Scholar
https://www.semanticscholar.org/paper/Graph-Connectivity-Kammer/8b0cc766664b976c43a04fa617a6c1041c0fdd4e
Checking whether a graph is connected and finding all its connected components can be done in time O(n + m) using depth-first search (DFS) or breadth-first ...
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45 Graph Connectivity and Network Coding
https://cs.uwaterloo.ca/~lapchi/papers/Hackson-thesis.pdf
In undirected graph, to completely split-off a vertex x, the simplest way is to try all O(d(x)2) pairs, and then check whether the edge connectivities are ...
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46 On Element-Connectivity Preserving Graph Simplification
https://chekuri.cs.illinois.edu/papers/elem-connectivity-esa.pdf
nonterminal vertices, check which one of the two operations preserves element-connectivity, reduce and repeat. For a graph on n vertices and m edges, ...
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47 Consider the following algorithm to check connectivity of a ...
https://homework.study.com/explanation/consider-the-following-algorithm-to-check-connectivity-of-a-graph-defined-by-its-adjacency-matrix-algorithm-connected-a-o-n-1-0-n-1-input-adjacency-matrix-a-o-n-1-0-n-1-of-an-undirected-gr.html
Adjacency matrix indicates whether the pairs of vertices is adjacent or not adjacent. It is said to be symmetric if the graph is un-directed. Answer and ...
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48 Connectivity and Biconnectivity
https://www.cs.purdue.edu/homes/ayg/CS251/slides/chap9d.pdf
CS 16: Connectivity ... connected not connected. Connected Component: maximal connected subgraph of a graph ... test resulting graph for connectivity;.
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49 An Algorithm for Determining Whether the ... - ProQuest
http://search.proquest.com/openview/2d686fb5924a4960feef44a85b324885/1?pq-origsite=gscholar&cbl=666313
The algorithm presented in this paper is for testing whether the connectivity of a large graph of $n$ vertices is at least $k$. First the case of undirected ...
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50 Rubber bands, convex embeddings and graph connectivity
https://www.cs.huji.ac.il/~nati/PAPERS/rubber_bands.pdf
Is there a more compact ,'proof" of k-connectivity, say, an additional structure whose presence gives a trivially check- able proof of k-connectivity? For k= 1, ...
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51 Network Flow and Testing Graph Connectivity
https://www.cs.umd.edu/~gasarch/BLOGPAPERS/even-tarjan.pdf
NETWORK FLOW AND TESTING GRAPH CONNECTIVITY*. SHIMON EVENT AND R. ENDRE TARJAN‡. Abstract. An algorithm of Dinic for finding the maximum flow in a network ...
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52 Undirected Connectivity in Log-Space∗ - Omer Reingold
https://omereingold.files.wordpress.com/2014/10/sl.pdf
tant test case for understanding the tradeoff between two central resources ... Graph connectivity problems and space-bounded derandomization are the focus ...
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53 Connectivity check in 3-connected planar graphs with ... - LaBRI
https://www.labri.fr/perso/courcell/Conferences/TGGT.pdf
We define a vertex labelling for every planar 3-connected graph with n vertices from which one can answer connectivity queries. A connectivity query asks ...
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54 Graph Theory and NetworkX - Part 2: Connectivity and Distance
https://walkenho.github.io/graph-theory-and-networkX-part2/
An undirected graph is called connected if you can get from every node to every other node in the network. A graph where this is not possible is ...
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55 Vertex connectivity. - R
https://search.r-project.org/CRAN/refmans/igraph/html/vertex_connectivity.html
Logical constant. Whether to check that the graph is connected and also the degree of the vertices. If the graph is not (strongly) connected then the ...
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56 Introduction to Testing Graph Properties
http://www.wisdom.weizmann.ac.il/~oded/COL/tgp-intro.pdf
1), non-adaptive testers in the bounded-degree graph model (Appendix A.2), and testing strong connectivity of directed graphs by only using forward queries ( ...
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57 BFS and Undirected Connectivity - Week 1 | Coursera
https://www.coursera.org/lecture/algorithms-graphs-data-structures/bfs-and-undirected-connectivity-BTVWn
Video created by Stanford University for the course "Graph Search, ... So I'll leave it for you to do the simple check that this squiggle is indeed an ...
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58 Testing Eulerianity and connectivity in directed sparse graphs
https://core.ac.uk/download/pdf/82175778.pdf
analysis of the testing algorithm for k-vertex-connectivity in bounded-degree undirected graphs that was shown by Yoshida and Ito [Y. Yoshida, H. Ito, ...
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59 Using expander graphs to find vertex connectivity
https://www.researchgate.net/publication/220431595_Using_expander_graphs_to_find_vertex_connectivity
The (vertex) connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial.
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60 Weakly Connected Components - Neo4j Graph Data Science
https://neo4j.com/docs/graph-data-science/current/algorithms/wcc/
One study uses WCC to work out how well connected the network is, and then to see whether the connectivity remains if 'hub' or 'authority' nodes are moved ...
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61 Dynamic connectivity problem - Codeforces
https://codeforces.com/blog/entry/15296
We were given a graph and a set of queries like "suppose we removed from the graph k ≤ 4 edges. Check whether graph is still connected?
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62 Strongly connected components - ICS, UCI
https://www.ics.uci.edu/~eppstein/161/960220.html
Strong connectivity and equivalence relations ... In undirected graphs, two vertices are connected if they have a path connecting them. How should we define ...
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63 Strongly Connected Components Tutorials & Notes | Algorithms
https://www.hackerearth.com/practice/algorithms/graphs/strongly-connected-components/tutorial/
Connectivity in an undirected graph means that every vertex can reach every other vertex via any path. If the graph is not connected the graph can be broken ...
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64 Adaptive Parallel Computation of Graph Connectivity Queries
https://www2.seas.gwu.edu/~howie/publications/Aquila-HPDC20.pdf
Graph connectivity algorithms answer whether two nodes in a ... this pivot, and check whether the XCC size equals to the graph size [21].
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65 Lecture 8: Undirected Connectivity is in logspace
https://www.tifr.res.in/~prahladh/teaching/05spring/lectures/lec8.pdf
between two specified vertices in a given undirected graph. ... check (s, t) connectivity is a d16-regular non-bipartite graph.
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66 Connectivity: Definition, Graph Theory with Solved Problems
https://testbook.com/learn/maths-connectivity/
Properties of Connectivity · A connected graph is also called an undirected graph with at least one connecting path between a pair of vertices.
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67 Testing connectivity when deleting an edge - MathOverflow
https://mathoverflow.net/questions/52410/testing-connectivity-when-deleting-an-edge
I would say yes. If the connectivity between x and y has decreased, then obviously the connectivity of G has decreased. On the other hand, if G−e ...
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68 Faster dynamic algorithms and sensitivity oracles for graph ...
https://lsa.umich.edu/content/dam/math-assets/math-document/reu-documents/ugradreu/2021/J.Gao_REU21.pdf
The project aims to find faster algorithms to check the k−edge(and k−vertex) connectivity between all pairs of vertices when given a graph.
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69 Lecture 4: Random Walks 1 Graph Connectivity
https://people.seas.harvard.edu/~salil/cs225/spring07/lecnotes/lec4.pdf
One of the most basic problems in computer science is that of deciding connectivity in graphs, i.e.. S-T Connectivity: Given a directed graph G ...
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70 2-Connected Graphs Definition 1
http://www.cs.rpi.edu/~goldberg/14-GT/08-block.pdf
A separating set or vertex cut of a connected graph G is a set. S ⊂ V (G) such that G − S is disconnected. The connectivity of G, denoted κ(G) is the ...
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71 Algebraic Connectivity and Graph Robustness - OSTI.gov
https://www.osti.gov/servlets/purl/973665-U3niHw/
graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic ... the function graph_connected(A) checks the adjacency matrix.
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72 Connectivity In Graph Theory - Definition and Examples
https://byjus.com/maths/connectivity/
Connectivity is one of the essential concepts in graph theory. A graph may be related to either connected or disconnected in terms of topological space. If ...
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73 Dynamic Spanning Trees for Connectivity Queries on Fully ...
https://www.vldb.org/pvldb/vol15/p3263-chen.pdf
A fundamental problem is the connectivity problem, which checks if there is a connection between two nodes in a graph. Answering connectivity queries.
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74 a new linear algorithm for checking a graph
http://cobweb.cs.uga.edu/~rwr/STUDENTS/fsunms.pdf
A new algorithm to test an arbitrary graph for 3-edge-connectivity is proposed, ... graph. Testing was done on simple graphs and Feynman diagrams.
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75 Chapter 5 Connectivity
http://www-sop.inria.fr/members/Frederic.Havet/Cours/connectivity.pdf
Reciprocally, the edge-connectivity of a graph cannot be bounded by its ... It is simple matter to check that the paths P 1,...,P k,P k+1 satisfy the ...
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76 Constructing Expanders, Undirected Connectivity in log space
https://sites.math.rutgers.edu/~sk1233/courses/topics-S13/lec11.pdf
Today we know many constructions of constant degree expander graphs. ... As in Savitch's algorithm, we try to improve “connectivity” of G, test s-t.
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77 Testing 2-vertex connectivity and computing pairs of vertex ...
https://www.cs.uoi.gr/~loukas/index.files/2-vertex-connectivity.pdf
Our algorithm is based on a new characterization of 2-vertex connected directed graphs, based on the concept of dominators in flowgraphs. A flowgraph G(s)=(V,A, ...
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78 Chapter 2 Graphs - Green Tea Press
https://greenteapress.com/complexity2/html/thinkcomplexity2003.html
Graphs are also useful, because there are many real world problems that can be solved using graph algorithms. For example, Dijkstra's shortest path algorithm is ...
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79 2-Edge Connectivity in Directed Graphs - ACM Digital Library
https://dl.acm.org/doi/10.1145/2968448
Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected ...
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80 A Polynomial Time Algorithm to Determine Singly Connectivity ...
https://ijarcce.com/wp-content/uploads/2015/12/IJARCCE-85.pdf
... time to check it. Keywords: DFS; source vertex; cyclic; tree; spanning forest. I. INTRODUCTION. Graph connectivity has become a widely studied property.
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81 Sufficient Conditions for Graphs to Be -Connected, Maximally ...
https://www.hindawi.com/journals/complexity/2021/5588146/
Let be a connected graph with minimum degree and vertex-connectivity . The graph is -connected if , maximally connected if , and ...
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82 15.4 Connectivity and Recursive Graph Traversal
https://www.cs.toronto.edu/~david/course-notes/csc110-111/15-graphs/04-connectivity-and-recursive-graph-traversal.html
Our goal in this section will be to implement a generalization of this method that goes from checking whether two vertices are adjacent to whether two vertices ...
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83 A New Perspective on Vertex Connectivity - People
https://people.csail.mit.edu/ghaffari/papers/Vertexconn.pdf
Vertex and edge connectivity are two core graph-theoretic concepts as they ... Let us first check the case of short connector paths, which is performed in ...
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84 Boost Graph Library: Connected Components - 1.79.0
https://www.boost.org/doc/libs/1_79_0/libs/graph/doc/connected_components.html
A connected component of an undirected graph is a set of vertices that are all reachable from each other. If the connected components need to be maintained ...
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85 scipy.sparse.csgraph.connected_components
https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csgraph.connected_components.html
Nodes i and j are strongly connected if a path exists both from i to j and from j to i. A directed graph is weakly connected if replacing all of its directed ...
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86 GRAPH CONNECTIVITIES, NETWORK CODING, AND ... - USC
http://www-scf.usc.edu/~hoyeeche/papers/connectivity.pdf
Graph connectivity is a basic concept that measures the reli- ... and check whether the edge connectivities decrease for some pairs after its splitting-.
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87 Constructing Minimally 3-Connected Graphs - MDPI
https://www.mdpi.com/1999-4893/14/1/9/htm
To test sets of vertices and edges for 3-compatibility, which depends on the cycles of the graph, we develop a method for obtaining the cycles of G ′ from the ...
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88 Using Expander Graphs to Find Vertex Connectivity 1 ...
https://home.cs.colorado.edu/~hal/Papers/expandersC.ps.gz
Here is a simple example illustrating how expanders can help nd vertex connectivity: Suppose. in an undirected graph G = (V; E) we want to check that any ...
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89 Undirected Graphs - Algorithms, 4th Edition
https://algs4.cs.princeton.edu/41graph/
A path in a graph is a sequence of vertices connected by edges, ... Brute force: delete edge (or vertex) and check connectivity.
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90 3.5 Connectivity in Directed Graphs - RIT
https://www.cs.rit.edu/~rlaz/algorithms20082/slides/DAGs.pdf
Strong Connectivity. Def. Node u and v are mutually reachable if there is a path from u to v and also a path from v to u. Def. A graph is strongly connected ...
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91 Measuring connectivity with graph Laplacian eigenvalues
https://www.johndcook.com/blog/2016/01/07/connectivity-graph-laplacian/
Measuring how connected a graph is by looking at the size of the second eigenvalue of the graph Laplacian.
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92 Create Graph online and find shortest path or use other ...
https://graphonline.ru/en/
Create graph online and use big amount of algorithms: find the shortest path, find adjacency matrix, find minimum spanning tree and others.
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93 How To Check Simple Connectivity In Graph? - ADocLib
https://www.adoclib.com/blog/how-to-check-simple-connectivity-in-graph.html
How To Check Simple Connectivity In Graph? An undirected graph G is therefore disconnected if there exist two vertices in G such that no path in G has these ...
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