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Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks.

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The authors' code

Fortran · 443 lines · 19 KB · LGPL-3.0

  1. program simple_network_example_p
  2. use hyperSIS_kinds_mod, only: dp, i4, fmt_general
  3. use hyperSIS_network_mod, only : network_t
  4. use hyperSIS_dynamics_mod, only: dyn_parameters_t, net_state_base_t, net_state_choose
  5. use hyperSIS_program_common_mod, only: read_network, set_dyn_params, check_qs_method, proc_net_state_gen, proc_export_states, check_export_nodes_and_edges_state, set_initial_number_of_infected_nodes
  7. use datastructs_mod, only: measure_controller_t, statistical_measure_t
  9. use rndgen_mod, only: rndgen
  11. use datastructs_mod, only: log_write, set_level, set_verbose, LOGGER_OK, LOG_ERROR, LOG_WARNING, LOG_INFO, LOG_DEBUG
  12. implicit none
  14. ! Network and dynamics variables
  15. type(network_t) :: net
  16. type(dyn_parameters_t) :: dyn_params
  17. class(net_state_base_t), allocatable :: dynamics_state
  18. procedure(proc_net_state_gen), pointer :: after_dynamics_step => null()
  19. procedure(proc_export_states), pointer :: export_states => null()
  21. ! Random number generator
  22. type(rndgen) :: dyn_gen
  24. ! Auxiliary variables
  25. integer(kind=i4) :: i, i_sample
  27. ! Parameters (via CLI)
  28. logical :: logger_verbose
  29. character(len=:), allocatable :: logger_level
  31. integer(kind=i4) :: rnd_seed
  32. integer(kind=i4) :: n_samples
  33. integer(kind=i4) :: initial_number
  34. character(len=:), allocatable :: output_prefix, edges_file, algorithm, sampler_choice, time_scale
  35. real(kind=dp) :: par_b, par_theta, initial_infected_fraction, beta_1, tmax
  36. logical :: use_qs, use_example_network, export_states_flag
  38. ! Measurers
  39. type(measure_controller_t) :: time_control
  40. type(statistical_measure_t) :: time_average
  41. type(statistical_measure_t) :: rho_average
  43. ! Get input data
  44. call handle_cli()
  46. ! Initialize main structures (network, parameters, measurers)
  47. call init_main()
  49. ! Loop over dynamics samples
  50. do i_sample = 1, n_samples
  51. ! Allocate dynamics state
  52. call init_dynamics(i_sample + (n_samples + 1))
  54. ! Run the dynamics up to time tmax, while there are infected nodes
  55. call loop_over_time()
  57. ! Write results to a file
  58. call write_results()
  60. ! Deallocate dynamics state for the next sample
  61. deallocate(dynamics_state)
  62. end do
  64. contains
  66. subroutine handle_cli()
  67. use flap, only : command_line_interface
  68. type(command_line_interface) :: cli ! Command Line Interface (CLI)
  69. character(len=2048) :: cli_string
  70. integer(kind=i4) :: cli_error
  72. call cli%init(progname = 'Run temporal dynamics on a hypergraph network', &
  73. description = 'This program runs a temporal dynamics on a hypergraph network, using the Gillespie algorithm. The network can be read from a file or generated as a small example. The dynamics can be configured with various parameters.', &
  74. version = '1.0', &
  75. authors = 'Wesley Cota')
  77. ! Add options to the CLI
  78. ! IO parameters
  79. call cli%add(switch='--output', &
  80. switch_ab='-o', &
  81. help='Output prefix for result files', &
  82. required=.false., &
  83. act='store', &
  84. def='./output', &
  85. error=cli_error); if (cli_error /= 0) error stop 'Error adding --output'
  86. call cli%add(switch='--remove-files', &
  87. switch_ab='-rm', &
  88. help='Remove existing output files before running', &
  89. required=.false., &
  90. act='store', &
  91. def='false', &
  92. error=cli_error); if (cli_error /= 0) error stop 'Error adding --remove-files'
  93. call cli%add(switch='--edges-file', &
  94. switch_ab='-e', &
  95. help='File containing the edge list of the network as input', &
  96. required=.false., &
  97. act='store', &
  98. def='', &
  99. error=cli_error); if (cli_error /= 0) error stop 'Error adding --edges-file'
  101. ! Dynamics and sampler
  102. call cli%add(switch='--algorithm', &
  103. switch_ab='-a', &
  104. help='Dynamics algorithm to use', &
  105. required=.false., &
  106. act='store', &
  107. choices='HB_OGA,NB_OGA', &
  108. def='HB_OGA', &
  109. error=cli_error); if (cli_error /= 0) error stop 'Error adding --algorithm'
  110. call cli%add(switch='--sampler', &
  111. switch_ab='-s', &
  112. help='Sampler choice', &
  113. required=.false., &
  114. act='store', &
  115. choices='rejection_maxheap,btree', &
  116. def='rejection_maxheap', &
  117. error=cli_error); if (cli_error /= 0) error stop 'Error adding --sampler'
  119. ! Temporal parameters
  120. call cli%add(switch='--tmax', &
  121. switch_ab='-t', &
  122. help='Maximum simulation time', &
  123. required=.false., &
  124. act='store', &
  125. def='1000.0', &
  126. error=cli_error); if (cli_error /= 0) error stop 'Error adding --tmax'
  127. call cli%add(switch='--use-qs', &
  128. switch_ab='-qs', &
  129. help='Use Quasi-Stationary method', &
  130. required=.false., &
  131. act='store', &
  132. def='false', &
  133. error=cli_error); if (cli_error /= 0) error stop 'Error adding --use-qs'
  135. ! Sampling and statistics
  136. call cli%add(switch='--n-samples', &
  137. switch_ab='-ns', &
  138. help='Number of samples to average over', &
  139. required=.false., &
  140. act='store', &
  141. def='10', &
  142. error=cli_error); if (cli_error /= 0) error stop 'Error adding --n-samples'
  143. call cli%add(switch='--time-scale', &
  144. switch_ab='-ts', &
  145. help='Time scale to use', &
  146. required=.false., &
  147. act='store', &
  148. choices='powerlaw,uniform', &
  149. def='powerlaw', &
  150. error=cli_error); if (cli_error /= 0) error stop 'Error adding --time-scale'
  152. ! Dynamical parameters
  153. call cli%add(switch='--initial-fraction', &
  154. switch_ab='-if', &
  155. help='Initial fraction of infected nodes', &
  156. required=.false., &
  157. act='store', &
  158. def='1.0', &
  159. error=cli_error); if (cli_error /= 0) error stop 'Error adding --initial-fraction'
  160. call cli%add(switch='--initial-number', &
  161. switch_ab='-in', &
  162. help='Initial number of infected nodes (overrides initial-fraction)', &
  163. required=.false., &
  164. act='store', &
  165. def='0', &
  166. error=cli_error); if (cli_error /= 0) error stop 'Error adding --initial-number'
  167. call cli%add(switch='--beta1', &
  168. switch_ab='-b1', &
  169. help='Infection rate parameter beta1', &
  170. required=.true., &
  171. act='store', &
  172. error=cli_error); if (cli_error /= 0) error stop 'Error adding --beta1'
  173. call cli%add(switch='--par-b', &
  174. switch_ab='-pb', &
  175. help='Dynamical parameter b', &
  176. required=.false., &
  177. act='store', &
  178. def='0.5', &
  179. error=cli_error); if (cli_error /= 0) error stop 'Error adding --par-b'
  180. call cli%add(switch='--par-theta', &
  181. switch_ab='-pt', &
  182. help='Dynamical parameter theta', &
  183. required=.false., &
  184. act='store', &
  185. def='0.5', &
  186. error=cli_error); if (cli_error /= 0) error stop 'Error adding --par-theta'
  188. ! Additional parameters
  189. call cli%add(switch='--export-states', &
  190. switch_ab='-es', &
  191. help='Export the states of nodes and edges at the end of each sample (be careful with large networks)', &
  192. required=.false., &
  193. act='store', &
  194. def='false', &
  195. error=cli_error); if (cli_error /= 0) error stop 'Error adding --export-states'
  196. call cli%add(switch='--seed', &
  197. switch_ab='-rs', &
  198. help='Random seed for the dynamics', &
  199. required=.false., &
  200. act='store', &
  201. def='42', &
  202. error=cli_error); if (cli_error /= 0) error stop 'Error adding --seed'
  203. call cli%add(switch='--verbose', &
  204. switch_ab='-vv', &
  205. help='Enable verbose logging', &
  206. required=.false., &
  207. act='store', &
  208. def='true', &
  209. error=cli_error); if (cli_error /= 0) error stop 'Error adding --verbose'
  210. call cli%add(switch='--verbose-level', &
  211. switch_ab='-vl', &
  212. help='Logging level', &
  213. required=.false., &
  214. act='store', &
  215. choices='error,warning,info,debug', &
  216. def='info', &
  217. error=cli_error); if (cli_error /= 0) error stop 'Error adding --verbose-level'
  219. call cli%parse(error=cli_error); if (cli_error /= 0) error stop 'Error parsing command line arguments'
  221. ! Collect parameters from CLI
  222. call cli%get(switch='--output', val=cli_string, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --output'
  223. output_prefix = trim(adjustl(cli_string))
  224. call cli%get(switch='--remove-files', val=export_states_flag, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --remove-files'
  225. call cli%get(switch='--edges-file', val=cli_string, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --edges-file'
  226. edges_file = trim(adjustl(cli_string))
  227. call cli%get(switch='--algorithm', val=cli_string, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --algorithm'
  228. algorithm = trim(adjustl(cli_string))
  229. call cli%get(switch='--sampler', val=cli_string, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --sampler'
  230. sampler_choice = trim(adjustl(cli_string))
  231. use_example_network = (len_trim(edges_file) == 0)
  232. call cli%get(switch='--tmax', val=tmax, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --tmax'
  233. call cli%get(switch='--use-qs', val=use_qs, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --use-qs'
  234. call cli%get(switch='--n-samples', val=n_samples, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --n-samples'
  235. call cli%get(switch='--time-scale', val=cli_string, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --time-scale'
  236. time_scale = trim(adjustl(cli_string))
  237. call cli%get(switch='--initial-fraction', val=initial_infected_fraction, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --initial-fraction'
  238. call cli%get(switch='--initial-number', val=initial_number, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --initial-number'
  239. call cli%get(switch='--beta1', val=beta_1, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --beta1'
  240. call cli%get(switch='--par-b', val=par_b, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --par-b'
  241. call cli%get(switch='--par-theta', val=par_theta, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --par-theta'
  242. call cli%get(switch='--export-states', val=export_states_flag, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --export-states'
  243. call cli%get(switch='--seed', val=rnd_seed, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --seed'
  244. call cli%get(switch='--verbose', val=logger_verbose, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --verbose'
  245. call cli%get(switch='--verbose-level', val=cli_string, error=cli_error); if (cli_error /= 0) error stop 'Error parsing --verbose-level'
  246. logger_level = trim(adjustl(cli_string))
  248. call set_verbose(logger_verbose)
  249. select case (trim(adjustl(logger_level)))
  250. case ('error')
  251. call set_level(LOG_ERROR)
  252. case ('warning')
  253. call set_level(LOG_WARNING)
  254. case ('info')
  255. call set_level(LOG_INFO)
  256. case ('debug')
  257. call set_level(LOG_DEBUG)
  258. case default
  259. call set_level(LOG_INFO)
  260. end select
  262. if (len(edges_file) == 0) then
  263. use_example_network = .true.
  264. else
  265. use_example_network = .false.
  266. end if
  268. end subroutine
  270. subroutine init_main()
  272. call time_control%init(time_scale)
  273. call time_average%init(time_control%get_max_array_size(real(tmax,dp)))
  274. call rho_average%init(time_control%get_max_array_size(real(tmax,dp)))
  276. select case (use_example_network)
  277. case (.true.)
  278. ! Generate a simple network
  279. call generate_example_network(net)
  280. case (.false.)
  281. ! Read the network from a file
  282. call read_network(net, edges_file)
  283. end select
  285. ! Clear and check the network (always necessary)
  286. call net%clear_and_check_all(min_order=1)
  288. ! Set initial number of infected nodes if specified
  289. call set_initial_number_of_infected_nodes(net, initial_infected_fraction, initial_number)
  291. ! Set the dynamical parameters
  292. call set_dyn_params(net, dyn_params, par_b, par_theta)
  294. ! Check if the chosen QS method is compatible with the dynamics
  295. call check_qs_method(after_dynamics_step, use_qs)
  297. ! Check if the export states procedure is set
  298. call check_export_nodes_and_edges_state(export_states, export_states_flag)
  300. end subroutine init_main
  302. subroutine init_dynamics(extra_seed)
  303. integer(kind=i4), intent(in), optional :: extra_seed
  304. integer(kind=i4) :: seed_offset
  306. if (present(extra_seed)) then
  307. seed_offset = extra_seed
  308. else
  309. seed_offset = 0
  310. end if
  312. ! reset the time control
  313. call time_control%reset()
  314. call dyn_gen%init(rnd_seed + seed_offset) ! initialize the random generator with a seed
  316. ! select dynamics algorithm
  317. call net_state_choose(dynamics_state, algorithm)
  319. ! allocate and initializes the dynamics with a random configuration
  320. call dynamics_state%init_config(net=net, gen=dyn_gen, params=dyn_params, sampler_choice=sampler_choice, fraction=initial_infected_fraction)
  322. ! Set the beta scale parameter
  323. ! by default, alpha = 1.0
  324. dynamics_state%params%beta_scale = beta_1
  326. ! Initialize the dynamics
  327. call dynamics_state%dynamics_init(net)
  328. end subroutine init_dynamics
  330. subroutine loop_over_time()
  332. ! main dynamics loop
  333. do while (dynamics_state%time < tmax)
  335. ! get Gillespie time
  336. call dynamics_state%just_update_dt(net, dyn_gen)
  338. ! update the state
  339. call dynamics_state%dynamics_step(net, dyn_gen)
  341. ! do something after the dynamics step
  342. call after_dynamics_step(net, dynamics_state, dyn_gen)
  344. ! collect the new data
  345. call collect_data()
  347. ! leave if no infected nodes
  348. if (dynamics_state%get_num_infected() == 0) then
  349. call log_write(LOG_DEBUG, "No more events can occur, stopping the dynamics at t = ", dynamics_state%time)
  350. exit ! exit if no infected nodes
  351. end if
  352. end do
  353. end subroutine loop_over_time
  355. subroutine collect_data()
  356. integer(kind=i4), allocatable :: time_pos_array(:)
  357. integer(kind=i4) :: time_pos
  359. !$omp critical
  360. time_pos_array = time_control%get_pos_array(dynamics_state%time)
  362. do time_pos = 1, size(time_pos_array)
  363. call time_average%add_point(time_pos_array(time_pos), dynamics_state%time)
  364. call rho_average%add_point(time_pos_array(time_pos), 1.0_dp * dynamics_state%get_num_infected() / net%num_nodes)
  366. call export_states(net, dynamics_state, get_filename('states_nodes.dat'), get_filename('states_edges.dat'))
  367. end do
  368. !$omp end critical
  370. end subroutine collect_data
  372. subroutine write_results()
  373. integer(kind=i4) :: unidade_arquivo
  374. integer(kind=i4) :: time_pos
  376. !$omp critical
  377. ! write time average
  378. open(newunit=unidade_arquivo, file=get_filename('results.dat'), status='replace', action='write', form='formatted')
  379. ! write even when not finished
  380. ! For that, we need to know the maximum number of samples
  382. write(unidade_arquivo, fmt_general) '# Number of samples: ', time_average%max_n_samples
  383. write(unidade_arquivo, fmt_general) '# time', 'rho', 'rho_variance', 'n_samples'
  384. do time_pos = 1, time_control%get_max_array_size(real(tmax,dp))
  385. if (rho_average%n_samples(time_pos) > 0) then
  386. ! We use `use_max=.true.` since the missing samples have zero infected nodes
  387. write(unidade_arquivo, fmt_general) time_average%get_mean(time_pos), rho_average%get_mean(time_pos, use_max=.true.), rho_average%get_variance(time_pos, use_max=.true.), rho_average%n_samples(time_pos)
  388. end if
  389. end do
  390. close(unidade_arquivo)
  391. !$omp end critical
  393. end subroutine write_results
  395. subroutine generate_example_network(net)
  396. use hyperSIS_network_mod, only : hyperedge, network
  397. type(network_t), intent(inout) :: net
  398. integer(kind=i4) :: edge_id, node_pos, node_id
  400. net = network(num_nodes = 10, num_edges = 7)
  402. net%edges(1) = hyperedge([1, 2, 3])
  403. net%edges(2) = hyperedge([2, 3, 4])
  404. net%edges(3) = hyperedge([4, 5])
  405. net%edges(4) = hyperedge([1, 5])
  406. net%edges(5) = hyperedge([6, 7, 8])
  407. net%edges(6) = hyperedge([1, 2, 3, 7, 8, 9])
  408. net%edges(7) = hyperedge([9, 10])
  410. net%nodes(:)%degree = 0
  412. ! for each edge, collect the degree of each node
  413. do edge_id = 1, net%num_edges
  414. do node_pos = 1, net%edges(edge_id)%order + 1
  415. node_id = net%edges(edge_id)%nodes(node_pos)
  416. net%nodes(node_id)%degree = net%nodes(node_id)%degree + 1
  417. end do
  418. end do
  420. ! allocate the arrays of edges for each node
  421. do node_id = 1, net%num_nodes
  422. allocate(net%nodes(node_id)%edges(net%nodes(node_id)%degree))
  423. net%nodes(node_id)%degree = 0 ! reset to use as position counter
  424. end do
  426. ! for each edge, fill the edges array of each node
  427. do edge_id = 1, net%num_edges
  428. do node_pos = 1, net%edges(edge_id)%order + 1
  429. node_id = net%edges(edge_id)%nodes(node_pos)
  430. net%nodes(node_id)%degree = net%nodes(node_id)%degree + 1
  431. net%nodes(node_id)%edges(net%nodes(node_id)%degree) = edge_id
  432. end do
  433. end do
  435. end subroutine generate_example_network
  437. function get_filename(filename) result(pathname)
  438. character(len=*), intent(in) :: filename
  439. character(len=256) :: pathname
  440. write(pathname, '(g0)') trim(adjustl(output_prefix))//'_'//trim(adjustl(filename))
  441. end function get_filename
  443. end program simple_network_example_p

hyperSIS_sampling.f90 at commit ecea142, under LGPL-3.0 · at the source

Overview

Authors: Hugo P Maia1, Wesley Cota1, Yamir Moreno2,3, Silvio C Ferreira1,4,5
ORCID iDs: Hugo P Maia, Wesley Cota, Yamir Moreno, Silvio C Ferreira
  1. Departamento de Física, Universidade Federal de Viçosa, Viçosa, MG Brazil
  2. Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza, Spain
  3. Department of Theoretical Physics, Faculty of Sciences, University of Zaragoza, Zaragoza, Spain
  4. National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro, Brazil
  5. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP Brazil
Institutions: Universidade Federal de Viçosa (Brazil); Universidad de Zaragoza (Spain); Instituto de Biocomputación y Física de Sistemas Complejos; Universidade de São Paulo (Brazil); Centro Brasileiro de Pesquisas Físicas (Brazil)
Journal: Nature communications, volume 17, issue 1, article 8665
Dates: received 27 November 2025; accepted 29 June 2026; published online 15 July 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41467-026-75402-0 · PMID 42457723 · PMCID PMC13490459 · OpenAlex W7168415193
Open access: gold, a free copy (OpenAlex)
Preprint: arxiv:2509.20174
Status: code verified
Categories: none (in silico) (organism)
Keywords: Complex networks, Biological physics
Topic: Complex Network Analysis Techniques (Statistical and Nonlinear Physics, Physics and Astronomy), according to OpenAlex
Funding: Ministerio de Ciencia, Innovación y Universidades (10.13039.501100011033, PID2023, PID2023-149409NB-I00, / AEI10.13039/501100011033, 13039, MICIU/AEI/ 10.13039/501,100,011,033 /, MICIU/AEI/10.13039, 10.13039, 13039/501100011033, 501100011033, MICIU/AEI/10); Fundação de Amparo à Pesquisa do Estado de São Paulo (AEI/10.13039/501100011033, 10.13039/501100011033, 25/24366-1, 408389/2024-9, MICIU/AEI/10.13039/501100011033); Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (MICIU/AEI/10.13039/501100011033); Conselho Nacional de Desenvolvimento Científico e Tecnológico (408775/2024-6, MICIU/AEI/10.13039/501100011033, 10.13039/501100011033, 408389/2024-9, 310984/2023-8, AEI/10.13039/501100011033); Fundação de Amparo à Pesquisa do Estado de Minas Gerais (APQ-01973-24, APQ-03079-24); Gobierno de Aragón (E36_23R, 501100011033, 10.13039/501100011033, MICIU/AEI/10.13039/501100011033); European Regional Development Fund (10.13039/501100011033, 13039/501100011033, MICIU/ AEI /10.13039/501100011033, AEI/10.13039/501100011033, 501100011033, MICIU/AEI/10, E36-23R, PID2023-149409NB-I00); Agencia Estatal de Investigación (AEI//10.13039/501100011033/, 501100011033, MICIU/AEI /10.13039/501100011033, 10.13039/501100011033, 13039, 13039/501100011033, PID2023, 10.13039, PID2023-149409NB-I00, AEI/10)
Citations: cited by 1 paper (Europe PMC); 59 references in the paper

Abstract

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gisc-ufv/hyperSIS

License: LGPL-3.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: ecea14277af316e9b48066f85532b03cdf98c6d6, 20 August 2026
Languages: Fortran (19), Python (6), Jupyter (2), JavaScript (2)
Size: 114 files, 29 scripts
Software Heritage: not archived
Found in: “Code availability”
Holds: README, license file, environment (python/pyproject.toml, python/setup.py), continuous integration, documentation, 2 notebooks
Not found: CITATION.cff, tests
Tools: NumPy (5 files), NetworkX (4 files), Matplotlib (2 files), seaborn (2 files)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
31 files
At the source: github.com/gisc-ufv/hyperSIS

Zenodo 20548808

License: LGPL-3.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: the references
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (5 files), NetworkX (4 files), Matplotlib (2 files), seaborn (2 files)
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
31 files
At the source:

Code availability statement

The paper has a code availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-75402-0.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 58 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

Datasets cited

Data availability statement

The paper has a data availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-75402-0.

Versions

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Version 2, 28 September 2026

  • Funding: added Ministerio de Ciencia, Innovación y Universidades: 10.13039.501100011033, PID2023, PID2023-149409NB-I00, / AEI10.13039/501100011033, 13039, MICIU/AEI/ 10.13039/501,100,011,033 /, MICIU/AEI/10.13039, 10.13039, 13039/501100011033, 501100011033, MICIU/AEI/10; Fundação de Amparo à Pesquisa do Estado de São Paulo: AEI/10.13039/501100011033, 10.13039/501100011033, 25/24366-1, 408389/2024-9, MICIU/AEI/10.13039/501100011033; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior: MICIU/AEI/10.13039/501100011033; Conselho Nacional de Desenvolvimento Científico e Tecnológico: 408775/2024-6, MICIU/AEI/10.13039/501100011033, 10.13039/501100011033, 408389/2024-9, 310984/2023-8, AEI/10.13039/501100011033; Fundação de Amparo à Pesquisa do Estado de Minas Gerais: APQ-01973-24, APQ-03079-24; Gobierno de Aragón: E36_23R, 501100011033, 10.13039/501100011033, MICIU/AEI/10.13039/501100011033; European Regional Development Fund: 10.13039/501100011033, 13039/501100011033, MICIU/ AEI /10.13039/501100011033, AEI/10.13039/501100011033, 501100011033, MICIU/AEI/10, E36-23R, PID2023-149409NB-I00; Agencia Estatal de Investigación: AEI//10.13039/501100011033/, 501100011033, MICIU/AEI /10.13039/501100011033, 10.13039/501100011033, 13039, 13039/501100011033, PID2023, 10.13039, PID2023-149409NB-I00, AEI/10

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 2 keywords, 32 references.

Cite

This paper

Maia, H. P., Cota, W., Moreno, Y., & Ferreira, S. C. (2026). Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks. Nature communications, 17(1), 8665. https://doi.org/10.1038/s41467-026-75402-0

BibTeX

@article{maia2026efficient,
author = {Maia, Hugo P and Cota, Wesley and Moreno, Yamir and Ferreira, Silvio C},
title = {{Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks}},
journal = {Nature communications},
year = {2026},
month = jul,
volume = {17},
number = {1},
pages = {8665},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/s41467-026-75402-0},
url = {https://doi.org/10.1038/s41467-026-75402-0},
pmid = {42457723},
pmcid = {PMC13490459}
}

RIS

TY - JOUR
AU - Maia, Hugo P
AU - Cota, Wesley
AU - Moreno, Yamir
AU - Ferreira, Silvio C
TI - Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/07/15
VL - 17
IS - 1
SP - 8665
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/s41467-026-75402-0
UR - https://doi.org/10.1038/s41467-026-75402-0
LA - en
ER -

CSL-JSON

{
"id": "10.1038/s41467-026-75402-0",
"type": "article-journal",
"title": "Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks",
"container-title": "Nature communications",
"author": [
{
"family": "Maia",
"given": "Hugo P"
},
{
"family": "Cota",
"given": "Wesley"
},
{
"family": "Moreno",
"given": "Yamir"
},
{
"family": "Ferreira",
"given": "Silvio C"
}
],
"container-title-short": "Nat Commun",
"volume": "17",
"issue": "1",
"page": "8665",
"DOI": "10.1038/s41467-026-75402-0",
"PMID": "42457723",
"PMCID": "PMC13490459",
"ISSN": "2041-1723",
"publisher": "Nature Publishing Group",
"URL": "https://doi.org/10.1038/s41467-026-75402-0",
"language": "en",
"issued": {
"date-parts": [
[
2026,
7,
15
]
]
}
}

The tracing map gets a citation of its own once an author has validated it and it has a DOI.

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