Scale-free_network - Wikiparency

# Scale-free network  ## Microsims — three.js ### Scale-free network (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Scale-free_network.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Scale-free network — three.js microsim"></iframe> </div> **Open it full-screen:** [Scale-free_network.html](https://wikitube-3d-microsims.netlify.app/Scale-free_network.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Attractor]] - [[Bifurcation_theory]] - [[Catastrophe_theory]] - [[Dissipative_system]] - [[Hierarchy]] - [[Synchronization]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## MicroSim spec - **Recommended sim type:** network dynamics - **Microsimmability score:** 84/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Number of nodes` - `New edges per node` - `Highlight hubs` ### What animates Preferential attachment grows a network where a few hubs collect most links. ### Learning objective Show how preferential attachment yields hub-dominated networks. ## Links (Wikipedia order)  `Adjacency_list` · [[Adjacency_matrix]] · [[Agent-based_model]] · `Albert-László_Barabási` · `Alfréd_Rényi` · `Almost_surely` · `Assortativity` · `Balance_theory` · `Barabási–Albert_model` · `Bianconi–Barabási_model` · `Biological_network` · `Bipartite_graph` · `Blockmodeling` · `Boolean_network` · `Béla_Bollobás` · [[Centrality]] · `Clique_(graph_theory)` · `Clustering_coefficient` · [[Combinatorial_optimization]] · `Community_structure` · `Complete_graph` · `Complex_contagion` · `Complex_network` · `Computer_network` · `Cut_(graph_theory)` · `Cycle_(graph_theory)` · `Degree_(graph_theory)` · `Degree_distribution` · `Dependency_network` · `Derek_J._de_Solla_Price` · `Directed_graph` · `Distance_(graph_theory)` · `Dunbar's_number` · `Efficiency_(network_science)` · `Erdős_number` · `Erdős–Rényi_model` · `Evolving_network` · `Exponential_family_random_graph_models` · `Fitness_model_(network_theory)` · `Flow_network` · `Friendship_paradox` · `Gamma_function` · `Graph_(abstract_data_type)` · `Graph_(discrete_mathematics)` · `Graph_drawing` · `Group_centrality` · `Heavy-tailed_distribution` · `Hierarchical_network_model` · `Homophily` · `Hyperbolic_geometric_graph` · `Hypergraph` · `Incidence_matrix` · `Interdependent_networks` · `Internet` · `Lancichinetti–Fortunato–Radicchi_benchmark` · `Link_analysis` · `List_of_algorithms` · `List_of_network_scientists` · `List_of_network_theory_topics` · `Loop_(graph_theory)` · `Maximum-entropy_random_graph_model` · `Metrics_(networking)` · `Modularity_(networks)` · `Multigraph` · `Neighbourhood_(graph_theory)` · `Network_controllability` · `Network_effect` · [[Network_motif]] · `Network_on_a_chip` · [[Network_science]] · `Network_security` · [[Network_theory]] · `Node_(networking)` · `Non-linear_preferential_attachment` · `Normal_distribution` · `Pareto_distribution` · `Path_(graph_theory)` · `Paul_Erdős` · `Percolation_theory` · `Power_law` · `Preferential_attachment` · `Price's_model` · [[Probability_density_function]] · `Protein–protein_interaction` · `Random_geometric_graph` · `Random_graph` · `Reciprocity_(network_science)` · `Réka_Albert` · `Scale_invariance` · `Scale_parameter` · [[Science_(journal)]] · `Scientific_collaboration_network` · `Self-similarity` · `Semantic_network` · `Sidney_Redner` · `Six_Degrees_of_Kevin_Bacon` · `Six_degrees_of_separation` · [[Small-world_network]] · `Social_capital` · `Social_influence` · `Social_network` · `Social_network_analysis_software` · `Soft_configuration_model` · `Spatial_network` · `Stochastic_block_model` · `Telecommunications_network` · `Transitive_relation` · `Triadic_closure` · `UPA_model` · `University_of_Notre_Dame` · `Vertex_(graph_theory)` · `Watts–Strogatz_model` · `Webgraph` · `World_Wide_Web` > p5.js MicroSim stub · part of Systems Thinking · [Wikipedia source](https://en.wikipedia.org/wiki/Scale-free_network) > Relation: subfield of systems thinking. ## Concept summary A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as ## Build checklist - [ ] Claim it: set `status: in-progress` + `lease` + `leased_at` - [ ] Write the child page explaining the concept (tie it back to systems thinking) - [ ] Finalize parameter ranges and defaults - [ ] Implement the p5.js sketch (drawing + control regions) - [ ] Add caption + the learning objective on the page - [ ] Set `status: done` ## p5.js sketch ```javascript // MicroSim: Scale-free network let controls = {}; function setup() { // createCanvas(...); create sliders for the parameters above. } function draw() { // background(...); read controls; render network dynamics; respond live. } ``` --- Back to Systems Thinking · Wikipedia: [Scale-free network](https://en.wikipedia.org/wiki/Scale-free_network) ---  ## Semiotic profile > *The semiotic universals this article invokes, machine-derived from the crossref — **unverified** (born so). Populated 2026-07-06 for the Systems room.* **Universals (6):** 🟢 network (29) · 🟡 system (10) · 🟡 science (5) · 🟢 distribution (3) · 🟢 saturation (2) · 🟢 self similarity (2) **Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Scale-free_network) : [Wikitube](https://en.wikitube.io/wiki/Scale-free_network) ## Previous hub tags Tree parents: [[Complex_system]] · [[Cybernetics]] · [[Emergence]] · [[Feedback]] · [[Network_theory]] · [[Self-organization]] · [[Systems_science]] · [[Systems_theory]]. Legacy hubs: none. --- *Sources: 2 legacy notes. Minted wave 1, 2026-07-30 (v1.6 order).*