https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Graphs and Networks sorted by active. https://community.wolfram.com/groups/-/m/t/3631132 Hello everyone, I am developing a model of spacetime that shares some fundamental concepts with the Wolfram Physics Project but introduces a specific focus on testability and quantum noise signatures. In my theory, spacetime is represented as a finite directed quantum graph. The core idea is that the connectivity of the graph isn't just an abstract representation but directly dictates the physical observables we see in quantum systems. Key features of the model: Discrete Topology: Nodes represent Planck-scale events, and directed edges represent causal relationships. Emergent Physics: I have derived that the Einstein field equations and Maxwell's equations emerge as a low-energy limit of these graph dynamics. Experimental Predictions: Most importantly, the model predicts specific spectral signatures in the decoherence noise of current NISQ-era quantum processors and anomalies in high-energy particle scattering. Iam looking for collaborators who are interested in: Visualizing the graph dynamics using the Wolfram Language. Simulating the noise patterns to compare them with existing data from IBM or Google quantum hardware. I believe that by identifying the right "rewrite rules" for this directed graph, we can bridge the gap between discrete spacetime models and experimental verification. Looking forward to your feedback and potential collaboration! Sergej Materov 2026-01-30T11:52:49Z https://community.wolfram.com/groups/-/m/t/3761691 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/e71d5af0-8a32-4917-88a2-a42a5fbf2416 Robert Cowen 2026-07-16T17:09:06Z https://community.wolfram.com/groups/-/m/t/3773012 [![Four-color graphical bioinformatics: the machinery behind phylogenetic trees][1]][2] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Four-colorgraphicalbioinformatics.jpg&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Four-colorgraphicalbioinformatics.jpg&userId=20103 [3]: https://www.wolframcloud.com/obj/e19962d9-65ad-4946-a963-a0f1891c46c8 Jessica Alfonsi 2026-08-03T12:43:44Z https://community.wolfram.com/groups/-/m/t/3766927 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/b01ebfbb-4368-4ca6-8aca-cef36447cffa Robert Cowen 2026-07-23T13:27:44Z https://community.wolfram.com/groups/-/m/t/3755834 Wordle is a single-player word game acquired by the NY Times from inventor Josh Wardle about 4 years ago (https://www.nytimes.com/games/wordle). It is an English language elimination puzzle where the player attempts to determine a daily 5-letter answer word among a pool of 3,201 in 6 guesses from a pool of 14,855 5-letter guess words. There are several efficient strategies for solving the daily puzzle. The NYT game is popular, with over 4 million daily players in 2025. The wordle 5-clique problem is an intellectual curiosity and not considered an efficient solution method. It asks: what 5 word subsets of the 14,855 guess words contain 25 unique letters of the alphabet. The methodology used to solve the query follows. Computing was performed with Mathematica v.15 personal edition installed on an Intel i9-10900KF Windows 11 system overclocked to 5.1 GHz with 128 GB RAM. The current list of 14,855 guess words was obtained from https://gist.github.com/dracos/dd0668f281e685bad51479e5acaadb93 and converted to uppercase. The list was reduced in size to 9,365 words with 5 unique letters. sufficientWords = (If[Length[Union[Characters[#]]] == 5, #, Nothing] & /@ guessWords); Next, word pairs with no common letters were joined by undirected edges and placed in a dynamic array. Subsequently, the dynamic array was normalized to an ordinary list of 6,404,322 edges. edgesDA = CreateDataStructure["DynamicArray"]; Do[ iword = sufficientWords[[i]]; Do[ jword = sufficientWords[[j]]; If[! ContainsAny[Characters[iword], Characters[jword]], edgesDA["Append", iword \[UndirectedEdge] jword]], {j, i + 1, sufficientWordsCount} ], {i, 1, sufficientWordsCount - 1} ]; edges = Normal[edgesDA]; edgesDA = Null; (* 10 minutes *) The edges list was then placed in a graph: graph = Graph[edges]; (* 2 minutes *) from which the cliques were computed: all5cliques = FindClique[graph, {5}, All]; (* 1496 minutes *) Here are the 25 solutions: { {"VOZHD", "CIMEX", "GRYPT", "BLUNK", "WAQFS"} {"GLITZ", "PHYNX", "MOVED", "BRUCK", "WAQFS"} {"GLITZ", "PHYNX", "JOKED", "CRUMB", "WAQFS"} {"GLITZ", "PHYNX", "JUKED", "CROMB", "WAQFS"} {"GLITZ", "PHYNX", "DRECK", "JUMBO", "WAQFS"} {"GIZMO", "PHYNX", "VELDT", "BRUCK", "WAQFS"} {"VOZHD", "CLUNK", "GRYPT", "BEMIX", "WAQFS"} {"VOZHD", "XYLIC", "KEMPT", "BRUNG", "WAQFS"} {"FRITZ", "WHUMP", "GYVED", "BLONX", "JACKS"} {"MILTZ", "PHYNX", "GOVED", "BRUCK", "WAQFS"} {"MILTZ", "PHYNX", "JUDGE", "BROCK", "WAQFS"} {"KLUTZ", "PHYNX", "JIVED", "CROMB", "WAQFS"} {"KLUTZ", "PHYNX", "GIVED", "CROMB", "WAQFS"} {"JUMPY", "VOZHD", "TRECK", "BLING", "WAQFS"} {"JUMPY", "VOZHD", "GLENT", "BRICK", "WAQFS"} {"FRITZ", "JUMPS", "GYVED", "BLONX", "WHACK"} {"FRITZ", "JUMPS", "GYVED", "BLONX", "CHAWK"} {"JIMPY", "VOZHD", "GLENT", "BRUCK", "WAQFS"} {"FJORD", "NYMPH", "GUCKS", "VIBEX", "WALTZ"} {"FJORD", "GLITZ", "PHYNX", "WEMBS", "QUACK"} {"FJORD", "CHUNK", "GYMPS", "VIBEX", "WALTZ"} {"CYLIX", "VOZHD", "KEMPT", "BRUNG", "WAQFS"} {"VOZHD", "PLING", "TRECK", "JUMBY", "WAQFS"} {"PRICK", "VOZHD", "GLENT", "JUMBY", "WAQFS"} {"CLIPT", "VOZHD", "KRENG", "JUMBY", "WAQFS"} } Of these, the permutation {"WALTZ", "FJORD", "VIBEX", "CHUNK", "GYMPS"} is considered to contain the least uncommon words, ordered mostly from highest to lowest vowel frequencies in the answer word pool. ![letter frequencies figure][1] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=wordleWordsInitialLetterFrequenciesFigure.jpg&userId=1957361 Richard Frost 2026-07-10T21:40:42Z https://community.wolfram.com/groups/-/m/t/3675919 **Intro** A fundamental question keeps coming up for me: If biological evolution operates in astronomically large spaces, why is search computationally tractable at all? Even a modest protein corresponds to a combinatorial space that is effectively impossible to exhaustively explore. Yet evolution does not behave like an unconstrained random search. So what makes the space navigable? **Essay** In 1859, two different perspectives on complexity emerged. Bernhard Riemann revealed deep structural order underlying the distribution of prime numbers. Charles Darwin introduced a dynamical process of variation and selection. Modern biology has successfully developed Darwin’s framework. However, something is often left implicit: the assumption that the search space is already structured in a way that makes local exploration effective. From a purely combinatorial perspective, this is problematic. Under simple assumptions (independent variation, no bias), expected search time grows exponentially with the amount of required information. In that regime, evolution would be computationally intractable. But real systems do not operate in that regime. Instead, they appear to evolve within a highly structured, constrained subspace, where: functional states are not isolated viable configurations form connected regions local mutations can traverse meaningful paths This suggests that evolution can be framed as a constrained search problem, rather than a purely stochastic process. Evolution is not merely a process acting within a space — it is a process shaped by the structure of the space it can access. This shifts the central question: What determines that accessible space? **A Minimal Computational Model** To make this concrete, consider a simple toy model. We define: a sequence space a mutation operator a constraint that restricts transitions **Basic setup** L = 20; randomSeq[] := RandomInteger[{0, 1}, L]; mutate[s_] := ReplacePart[s, RandomInteger[{1, L}] -> 1 - #] & @ s; **Fitness function** fitness[s_] := Boole[Total[s] > 12]; **Constraint energy** energy[s_] := Total[ Map[If[# === {1, 1}, 0, 1] &, Partition[s, 2, 1]] ]; **Dynamics: constrained vs unconstrained** stepConstrained[s_] := Module[{s2 = mutate[s]}, If[constraint[s, s2], s2, s] ]; stepRandom[s_] := mutate[s]; **Search experiment** findFunctional[step_, max_] := Module[ {s = randomSeq[], t = 0}, While[t < max && !TrueQ[fitness[s] == 1], s = step[s]; t++; ]; t ]; trialsConstrained = Table[ findFunctional[stepConstrained, 1000], {50} ]; trialsRandom = Table[ findFunctional[stepRandom, 1000], {50} ]; **Visualization** Histogram[ {trialsRandom, trialsConstrained}, ChartLegends -> {"Random", "Constrained"}, PlotTheme -> "Scientific", Frame -> True ] **Interpretation** In many runs, the constrained dynamics reaches functional states faster — not because the system is explicitly guided toward a target, but because the structure of the space itself has changed. Even in this minimal model, a key effect emerges: Pure random mutation behaves like unstructured search Even a simple constraint dramatically reshapes accessibility The constraint does not “guide” the system toward solutions. Instead, it reshapes the space such that functional paths become possible in the first place. **Open Questions** This raises several structural questions: - How can we formally define a constraint operator in general systems? - Can constraint-induced subspaces be measured or classified? - How does connectivity emerge in high-dimensional spaces under constraints? - Do constrained systems exhibit characteristic spectral signatures (e.g., non-random eigenvalue statistics)? **Closing Thought** The difference between intractable search and effective evolution may not lie in time or randomness — but in the geometry of the accessible space itself. Maurice Crutzen 2026-04-07T09:31:01Z https://community.wolfram.com/groups/-/m/t/3769381 ![Centroidal Voronoi diagrams on sphere][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=CentroidalVoronoidiagramsonsphere.jpg&userId=20103 [2]: https://www.wolframcloud.com/obj/43c415d2-9250-403a-86f8-7e88404d01fd Denis Ivanov 2026-07-29T04:24:48Z https://community.wolfram.com/groups/-/m/t/3762683 ![One Droplet at a Time: How Entailment Graphs Condense][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Drop.bmp&userId=3760951 [2]: https://www.wolframcloud.com/obj/f726a950-eea9-445f-b912-ae5953c1da14 Alexandra Ciotau 2026-07-16T22:03:47Z https://community.wolfram.com/groups/-/m/t/3755323 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/74d75cb8-ea22-4e48-9dae-b138b3cc06bc Naman Taggar 2026-07-10T14:25:01Z https://community.wolfram.com/groups/-/m/t/3763898 ![Searching for d-3 Quantum Error Correcting Codes on a 27-qubit Superconducting Processor][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=heroimage.png&userId=3716623 [2]: https://www.wolframcloud.com/obj/5c30137b-03b9-437f-847a-b6f2ffa3fa7e Luis Cervantes 2026-07-17T14:17:23Z https://community.wolfram.com/groups/-/m/t/3761646 ![Classifying Defects in Cellular Automata][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Presentation1.png&userId=20103 [2]: https://www.wolframcloud.com/obj/2c03701a-b59b-4418-bd06-47cbf267d6c9 Myrto Terpsiadou 2026-07-16T15:00:13Z https://community.wolfram.com/groups/-/m/t/3763367 ![HyperVacuum: A Dimension-Agnostic Hypergraph Lattice Model of the Quantum Vacuum][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=post.png&userId=3759777 [2]: https://www.wolframcloud.com/obj/8d235032-1a33-4170-b616-70cbad15f0aa Federico Selleri 2026-07-17T07:17:01Z https://community.wolfram.com/groups/-/m/t/3762876 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/e4b74567-4b6a-4766-9fea-137b498f478f Paula Botella Andreu 2026-07-17T00:13:05Z https://community.wolfram.com/groups/-/m/t/3763652 ![Structure-Adaptive Evolutionary Framework for Navigating the Rule-space of Hypergraphs][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=poster_picture.png&userId=3760479 [2]: https://www.wolframcloud.com/obj/1804b84e-d758-47ed-ac93-51c89d7f4b4a Samuel Frerichs 2026-07-17T15:15:04Z https://community.wolfram.com/groups/-/m/t/3763609 ![Non-Projectional Rigidity in Finite-Axiom Theorem Spaces, and the System-135 Phenomenon][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-16at2.11.17%E2%80%AFAM.png&userId=3760764 [2]: https://www.wolframcloud.com/obj/05ec56d8-bd27-4c23-82df-337c528c3a7f Svet Ivanov 2026-07-17T09:46:15Z https://community.wolfram.com/groups/-/m/t/3763335 ![Evolving Circles: Adaptive Search in a Cellular Automaton Rule Space][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=her13.png&userId=3760096 [2]: https://www.wolframcloud.com/obj/127cd5bc-632e-4933-9e64-3170c8a8d69f Jhoan Eduardo Saldarriaga Serna 2026-07-17T05:45:23Z https://community.wolfram.com/groups/-/m/t/3763192 ![Quantum Thickening of Reversible Block Cellular Automata: Analyzing Paths from S4 to U(4)][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=qca_evo.gif&userId=3760870 [2]: https://www.wolframcloud.com/obj/de1358df-9549-400e-9027-d2d41947c8c2 Deniz Yoldas 2026-07-17T02:22:33Z https://community.wolfram.com/groups/-/m/t/3762980 ![Self-Replication in Rewriting Systems][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=SelfRepInRewritingSystems_Preview.png&userId=3607526 [2]: https://www.wolframcloud.com/obj/49160842-f976-4067-b604-48dcc01184ce Matheo Tripnaux 2026-07-16T23:33:35Z https://community.wolfram.com/groups/-/m/t/3761847 ![Emergent Continuum Behavior in Reversible Multiway Systems][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=actual_multiway_entropy_hero_square.png&userId=3760080 [2]: https://www.wolframcloud.com/obj/69079318-d6cc-4b19-ae8e-6ced6ab28c53 Muhammad Awal Tahiru 2026-07-16T18:24:10Z https://community.wolfram.com/groups/-/m/t/3762346 ![Learning Mechanics of Neural Network: Chaotic Pendulum Metaphor][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Picture_poster1.png&userId=3760386 [2]: https://www.wolframcloud.com/obj/e95023e2-1371-48e9-a2a6-bef42df107eb Jinming Zhang 2026-07-16T19:50:36Z