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Everything about Strongly connected component
Partition of a graph whose components are reachable from all vertices
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of a directed graph form a partition into subgraphs that are strongly connected themselves. It is possible to test the strong connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ(V + E)). Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Strongly connected componentA 5-minute orientation
- Skim a recent paper: A Granulation Strategy-Based Algorithm for Computing Strongly Connected Components in ParallelInfluential work since 2022
- Pick up a classic book: The Conspirators HierarchyThe most-reprinted book on the subject
- Read the landmark paper: Giant strongly connected component of directed networksCited 188 times
- Go sideways: Biconnected componentA closely related topic
- Go sideways: Bipolar orientationA closely related topic
📖 Definitions
Noun Given a directed graph, a maximal strongly connected subgraph.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Giant strongly connected component of directed networks
The Size of the Largest Strongly Connected Component of a Random Digraph with a Given Degree Sequence
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
Efficient Disk-Based Directed Graph Processing: A Strongly Connected Component Approach
Quasi-stationary distributions as centrality measures for the giant strongly connected component of a reducible graph
Isomorphic and strongly connected components
The largest strongly connected component in the cyclical pedigree model of Wakeley et al.
A strongly connected component search-based algorithm for the verification of time-interval diagnosability
🆕 Influential since 2022
A Granulation Strategy-Based Algorithm for Computing Strongly Connected Components in Parallel
Efficient parallel algorithm for finding strongly connected components based on granulation strategy
Bayesian Network Structure Learning Approach Based on Searching Local Structure of Strongly Connected Components
Incremental Detection of Strongly Connected Components for Scholarly Data
Accelerating Node Influence Computation via Integration of Strongly Connected Component Assignment and Reachability Computation
📚 Books worth reading
The Conspirators HierarchyJohn Coleman · 1992
Discrete mathematics for computer scienceGary Haggard · 2006- 📕Matrix reduction using the strongly connected components of a digraphJohn Rafferty · 1985
প্রোগ্রামিং কনটেস্টমোঃ মাহবুবুল হাসান · 2016
Object-oriented design measurementScott A. Whitmire · 1997
Waldara AnswersWilliam Swygard · 1975
survival companion for medical students, graduates and interns · 2014
A TOUR OF THE WORLDMalik Mansab Khan, Muhammad Rafique Abdul Aziz · 2025
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Biconnected component In graph theory, a biconnected component or block (sometimes known as a 2-connected component) is a maximal biconnected subgraph. Any connected graph decomposes…
- Bipolar orientation In graph theory, a bipolar orientation or st-orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that causes…
- Kosaraju's algorithm In computer science, Kosaraju-Sharir's algorithm (also known as Kosaraju's algorithm) is a linear time algorithm to find the strongly connected components…
- Tarjan's strongly connected components algorithm Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph…
- Path-based strong component algorithm In graph theory, the strongly connected components of a directed graph may be found using an algorithm that uses depth-first search in combination with…
- Bridge (graph theory) In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. Equivalently…
- Pseudoforest In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. That is, it is a system of vertices and…
- Planar separator theorem In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into…