Graph Theory on Jeanphilo Bloghttps://shio-chan-dev.github.io/jeanblog/tags/graph-theory/Recent content in Graph Theory on Jeanphilo BlogHugo -- 0.159.2en-usMon, 09 Feb 2026 10:00:28 +0800Dynamic Graphs and Incremental Computation: ACERS Guide to Incremental Shortest Path, Incremental PageRank, and Connectivity Maintenancehttps://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/90-dynamic-graph-incremental-computation/Mon, 09 Feb 2026 10:00:28 +0800https://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/90-dynamic-graph-incremental-computation/For real-world graph systems, this article systematically explains dynamic graph incremental algorithms: incremental shortest path, incremental PageRank, and connectivity maintenance. It focuses on three core engineering techniques: local recomputation, lazy updates, and approximate results.The Graph Centrality Trio: Degree, Betweenness, and Closeness - ACERS Engineering Analysishttps://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/50-graph-centrality-degree-betweenness-closeness/Mon, 09 Feb 2026 09:56:11 +0800https://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/50-graph-centrality-degree-betweenness-closeness/A systematic guide to the three core graph centrality metrics: Degree, Betweenness, and Closeness. The key engineering takeaway: most production systems prioritize Degree and approximate Betweenness, with clear complexity and rollout tradeoffs.Connected Components and Strongly Connected Components: Tarjan / Kosaraju ACERS Engineering Analysishttps://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/40-connected-components-and-scc-tarjan-kosaraju/Mon, 09 Feb 2026 09:50:22 +0800https://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/40-connected-components-and-scc-tarjan-kosaraju/A systematic guide to undirected Connected Components and directed SCCs, with emphasis on Tarjan (common in production) and Kosaraju, mapped to graph-database scenarios such as community pre-grouping, subgraph splitting, and partition hints.Shortest Path Core Trio: BFS, Dijkstra, and A* ACERS Engineering Breakdownhttps://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/20-shortest-path-bfs-dijkstra-astar-acers/Mon, 09 Feb 2026 09:48:00 +0800https://shio-chan-dev.github.io/jeanblog/dev/algorithm/graph/20-shortest-path-bfs-dijkstra-astar-acers/A full engineering walkthrough of the shortest-path core trio: BFS for unweighted graphs, Dijkstra for non-negative weights, and heuristic A*. Includes multi-source BFS, bidirectional search, path pruning, and runnable multi-language templates.