🌐 Networks at Graph Theory

Force-Directed GraphFruchterman-Reingold spring layout for Erdős-Rényi, Barabási-Albert and Watts-Strogatz… Minimum Spanning TreeStep-by-step animation of Kruskal's and Prim's MST algorithms on a weighted graph. Toggle… Network ResilienceBarabási–Albert scale-free and Erdős–Rényi random networks under targeted hub attack vs… Small-World Networks — Watts-StrogatzStart from a regular ring lattice and rewire edges with probability p: watch clustering and… Scale-Free Network — Barabási-Albert Preferential AttachmentBarabási-Albert preferential attachment: new nodes connect with probability proportional to… Network ScienceSwitch between Erdős–Rényi, Barabási–Albert and Watts–Strogatz graph models: force-directed… TCP Congestion ControlNewTCP's congestion window: slow-start doubling, AIMD increase, multiplicative decrease on loss… Max-Flow / Min-CutNewRun Ford–Fulkerson (Edmonds–Karp) step by step: BFS finds augmenting paths, pushes flow… Community Detection (Louvain)NewDetect communities by greedily maximizing modularity with the Louvain method. Watch local… Internet RoutingNewDistance-vector routing (Bellman–Ford/RIP) can count to infinity; link-state (Dijkstra/OSPF)… Critical Path (CPM/PERT)NewModel a project as a DAG: forward/backward pass computes ES/EF/LS/LF and slack; zero-slack… PageRankNewGoogle's original ranking algorithm: a page's score is (1−d)/N plus d times inbound… Topological Sort — Ordering a DAGNewOrder a DAG's vertices so every edge points forward. Watch Kahn's algorithm peel off… Floyd-Warshall — All-Pairs Shortest PathsNewFloyd-Warshall finds shortest paths between every vertex pair in O(V³) by relaxing through… Bipartite Matching — Augmenting PathsNewFind a maximum matching in a bipartite graph via augmenting paths flipping matched and… DNS Resolution — Recursive Lookup & CachingNewTrace a DNS lookup from resolver to root, TLD and authoritative servers, then watch TTL… Random Graph — Giant Component & Phase TransitionNewConstruct an Erdos-Renyi G(n,p) random graph: as average degree crosses 1, a giant connected… Network Percolation — Giant Component ThresholdNewAdd random edges to nodes and watch the giant connected component emerge at p_c = 1/N.… Viral Spread on Contact NetworkNewAn SIR epidemic on a heterogeneous contact network — hubs spread it faster. Adjust β, γ and…