Graph Algorithms: From Structural Exploration to Combinatorial Optimization

Graphs are the universal modeling language for "entities + relationships." This path builds three layers of capability (structural exploration, measurement, combinatorial optimization), covers classical algorithms (BFS/DFS, shortest paths, network flow), then converges on modern methods (random graph models, probabilistic graphical models, GNNs). The "explore → measure → optimize → model" arc reveals how one set of graph tools manifests across seemingly different engineering domains.

1. 1

   图算法全景图：从结构探索到组合优化

   Intermediate Coming Soon

   #graph-algorithms#overview
2. 2

   图上的通用迭代机器（上）：从数学问题到求解框架

   Advanced Coming Soon

   #graph-algorithms#iteration-machine#unified-framework#frontier#fixed-point#bellman-equation
3. 3

   图上的通用迭代机器（下）：范式、领域与边界

   Advanced Coming Soon

   #graph-algorithms#iteration-machine#paradigm-unification#gc-tricolor#dataflow-analysis#belief-propagation#gnn#semiring#convergence
4. 4

   BFS 与 DFS：图的两种基本呼吸方式

   Intermediate Coming Soon

   #graph-algorithms#bfs#dfs#traversal
5. 5

   连通性：图能拆成几块？

   Intermediate Coming Soon

   #graph-algorithms#connectivity#scc#tarjan#bridge#articulation-point
6. 6

   拓扑排序与 DAG：有依赖时的合法顺序

   Intermediate Coming Soon

   #graph-algorithms#topological-sort#dag#critical-path#dynamic-programming
7. 7

   欧拉与哈密顿：遍历的两种完备性

   Intermediate Coming Soon

   #graph-algorithms#euler-path#hamiltonian-path#np-complete#hierholzer
8. 8

   树上算法：图的特殊骨架

   Intermediate Coming Soon

   #graph-algorithms#tree#lca#diameter#centroid#heavy-light-decomposition#dominator-tree
9. 9

   最短路径：图上的距离

   Intermediate Coming Soon

   #graph-algorithms#shortest-path#dijkstra#bellman-ford#floyd-warshall#a-star
10. 10

    中心性：谁最重要？

    Intermediate Coming Soon

    #graph-algorithms#centrality#degree#betweenness#closeness#pagerank#eigenvector#katz
11. 11

    社区发现：哪些节点抱团？

    Intermediate Coming Soon

    #graph-algorithms#community-detection#modularity#louvain#label-propagation#k-core
12. 12

    相似性与同构：两个图/节点有多像？

    Intermediate Coming Soon

    #graph-algorithms#similarity#isomorphism#graph-kernel#wl-test
13. 13

    团与密子图：最紧密的子群

    Intermediate Coming Soon

    #graph-algorithms#clique#dense-subgraph#k-core#k-truss#independent-set#vertex-cover
14. 14

    最小生成树：最便宜地连通所有人

    Intermediate Coming Soon

    #graph-algorithms#minimum-spanning-tree#kruskal#prim#boruvka#greedy#matroid#union-find
15. 15

    网络流：管道能通多少？

    Intermediate Coming Soon

    #graph-algorithms#network-flow#max-flow#min-cut#ford-fulkerson#edmonds-karp#dinic
16. 16

    匹配：最优配对

    Intermediate Coming Soon

    #graph-algorithms#matching#bipartite-matching#hungarian-algorithm#hopcroft-karp#blossom#assignment-problem
17. 17

    着色与划分：最少几种颜色？

    Intermediate Coming Soon

    #graph-algorithms#graph-coloring#graph-partitioning#chromatic-number#greedy-coloring#dsatur#planarity#metis
18. 18

    NP-hard 与近似算法：当最优解算不出来

    Advanced Coming Soon

    #graph-algorithms#np-hard#approximation#tsp#christofides#lp-relaxation#fpt#treewidth#vertex-cover
19. 19

    随机图与网络模型：真实网络长什么样？

    Advanced Coming Soon

    #graph-algorithms#random-graphs#network-models#erdos-renyi#small-world#scale-free#power-law#network-science
20. 20

    概率图模型：图上的不确定性推理

    Advanced Coming Soon

    #graph-algorithms#probabilistic-graphical-models#bayesian-network#markov-random-field#belief-propagation#factor-graph#crf
21. 21

    图嵌入与图神经网络：把图变成向量

    Advanced Coming Soon

    #graph-algorithms#graph-embedding#gnn#deepwalk#node2vec#gcn#gat#graphsage
22. 22

    图建模案例集：这个问题其实是图问题

    Advanced Coming Soon

    #graph-algorithms#graph-modeling#applications#compilers#recommender-systems#bioinformatics#causal-inference#nlp#vlsi#social-networks#logistics