Abstract
An undirected graph is connected if there is a path between any pair of its vertices. In a digraph, connectivity implies there is a path between any two of its vertices in both directions. We start this chapter by defining the parameters of vertex and edge connectivity. We continue by describing algorithms to find cut-vertices and bridges of undirected graphs. We then review algorithms to find blocks of graphs and strongly connected components of digraphs. We describe the relationship between Connectivity, and network flows and matching and review sequential, parallel and distributed algorithms for all of the mentioned topics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aho AV, Hopcroft JE, Ullman JD (1983) Data Structures and Algorithms. Addison-Wesley
Akl SG (1989) The design and analysis of parallel algorithms. Prentice Hall, Englewood Cliffs, p 07632
Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms, 3rd edn. MIT Press, Cambridge
Esfahanian AH (1988) On the evolution of connectivity algorithms. In: Wilson R, Beineke L (eds) Selected topics in graph theory. Cambridge University Press, Cambridge
Esfahanian AH, Hakimi SL (1984) On computing the connectivities of graphs and digraphs. Networks 355–366
Even S (1979) Graph algorithms, Computer Science Press (Computer software engineering series). ISBN-10: 0914894218, ISBN-13: 978-0914894216
Even S, Tarjan RE (1975) Network flow and testing graph connectivity. SIAM J Comput 4:507–518
Fleischer L, Hendrickson B, Pinar A (2000) On identifying strongly connected components in parallel. Parallel and distributed processing, pp 505–511
Grama A, Karypis G, Kumar V, Gupta A (2003) Introduction to parallel computing, 2nd edn. Addison-Wesley, New York
Hopcroft J, Tarjan R (1973) Algorithm 447: efficient algorithms for graph manipulation. Commun ACM 16(6):372–378
Matula DW (1987) Determining edge connectivity in \(O(mn)\). In: Proceedings, 28th symposium on foundations of computer science, pp 249–251
McLendon W III, Hendrickson B, Plimpton SJ, Rauchwerger L (2005) Finding strongly connected components in distributed graphs. J Parallel Distrib Comput 65(8):901–910
Tarjan RE (1972) Depth first search and linear graph algorithms. SIAM J Comput 1(2):146–160
Tarjan RE (1974) A note on finding the bridges of a graph. Inf Process Lett 2(6):160–161
Whitney H (1932) Congruent graphs and the connectivity of graphs. Am J Math 54:150–168
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Erciyes, K. (2018). Connectivity. In: Guide to Graph Algorithms. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-73235-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-73235-0_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73234-3
Online ISBN: 978-3-319-73235-0
eBook Packages: Computer ScienceComputer Science (R0)