Connected component
A connected component is a maximal subgraph in which every pair of vertices is connected by a path.
Graph Neural Networks in Action
A connected component is a maximal set of graph nodes in which every pair of nodes is connected by a path.
- How it is used
- Uses component structure to validate graph data, understand topology, and select a modeling subgraph.
- How deep it goes
- Explains the definition, counts components, compares their metrics, and demonstrates extraction, without deriving connectivity algorithms.
- Examples
- Uses fraud, candidate social, and Amazon product co-purchaser graphs for component counts, sparse-graph analysis, and connectivity inspection.
- What you can do after
- Apply it via NetworkX to count components, compare their sizes, isolate the largest subgraph, and support graph EDA.
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Grokking Data Structures
A connected component is a maximal subgraph in which every pair of vertices is connected by a path.
- How it is used
- Groups vertices into mutually reachable regions when a graph is disconnected.
- How deep it goes
- Defines connectivity, contrasts weak and strong directed connectivity, and stops short of presenting a component-finding algorithm.
- Examples
- Uses separate Tiger and Lion clusters, then examines the Chicken’s effect on weak and strong connectivity.
- What you can do after
- Evaluate whether a graph is connected and identify how its vertices divide into connected regions.
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Related concepts
- disjoint setused by · A disjoint-set data structure maintains a partition of elements into nonoverlapping sets and supports finding set representatives and merging sets.
- subgraphkind of · A subgraph is a graph whose vertices and edges are subsets of those of another graph, with every included edge connecting included vertices.
- graphpart of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
- treekind of · A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.
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