{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T20:22:53Z","timestamp":1783023773889,"version":"3.54.6"},"reference-count":56,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T00:00:00Z","timestamp":1782432000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Expert Systems with Applications"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.eswa.2026.133401","type":"journal-article","created":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T16:15:54Z","timestamp":1782231354000},"page":"133401","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"PA","title":["Probing post-hoc reasoning in LLMs over multi-step pathfinding tasks"],"prefix":"10.1016","volume":"332","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-2406-465X","authenticated-orcid":false,"given":"Yaying","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1229-2368","authenticated-orcid":false,"given":"Siamak","family":"Layeghy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mahsa","family":"Baktashmotlagh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marius","family":"Portmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.eswa.2026.133401_bib0001","series-title":"International conference on pattern recognition","first-page":"287","article-title":"Can LLMs perform structured graph reasoning tasks?","author":"Agrawal","year":"2025"},{"key":"10.1016\/j.eswa.2026.133401_bib0002","series-title":"ACM SIGCOMM Computer communication review","first-page":"63","article-title":"A scalable, commodity data center network architecture","volume":"vol. 38","author":"Al-Fares","year":"2008"},{"key":"10.1016\/j.eswa.2026.133401_bib0003","series-title":"Passive and active measurement workshop","first-page":"45","article-title":"On the accuracy of the internet AS-level topology","author":"Al-Sheikh","year":"2004"},{"key":"10.1016\/j.eswa.2026.133401_bib0004","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2025.113371","article-title":"An intelligent recurrent neural network driven secured routing protocol for vehicular ad hoc networks","volume":"317","author":"Bagirathan","year":"2025","journal-title":"Knowledge-Based Systems"},{"issue":"5939","key":"10.1016\/j.eswa.2026.133401_bib0005","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1126\/science.1173299","article-title":"Scale-free networks: A decade and beyond","volume":"325","author":"Barab\u00e1si","year":"2009","journal-title":"Science"},{"issue":"5439","key":"10.1016\/j.eswa.2026.133401_bib0006","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Barab\u00e1si","year":"1999","journal-title":"Science"},{"issue":"1","key":"10.1016\/j.eswa.2026.133401_bib0007","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1090\/qam\/102435","article-title":"On a routing problem","volume":"16","author":"Bellman","year":"1958","journal-title":"Quarterly of Applied Mathematics"},{"key":"10.1016\/j.eswa.2026.133401_bib0008","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2025.113046","article-title":"Joint resource allocation and congestion-aware routing based on hybrid optimization in IoT","volume":"311","author":"Bhushan","year":"2025","journal-title":"Knowledge-Based Systems"},{"key":"10.1016\/j.eswa.2026.133401_bib0009","doi-asserted-by":"crossref","unstructured":"Chen, Q., Qin, L., Liu, J., Peng, D., Guan, J., Wang, P., Hu, M., Zhou, Y., Gao, T., & Che, W. (2025a). Towards reasoning era: A survey of long chain-of-thought for reasoning large language models. 2503.09567.","DOI":"10.1007\/s11432-025-4665-8"},{"key":"10.1016\/j.eswa.2026.133401_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.jnca.2025.104272","article-title":"Mteal: Network routing optimization of SD-WAN traffic engineering integrating multi-dimensional QoS metrics","author":"Chen","year":"2025","journal-title":"Journal of Network and Computer Applications"},{"issue":"4","key":"10.1016\/j.eswa.2026.133401_bib0011","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1137\/070710111","article-title":"Power-law distributions in empirical data","volume":"51","author":"Clauset","year":"2009","journal-title":"SIAM Review"},{"key":"10.1016\/j.eswa.2026.133401_bib0012","series-title":"Statistical power analysis for the behavioral sciences","author":"Cohen","year":"1988"},{"key":"10.1016\/j.eswa.2026.133401_bib0013","series-title":"Introduction to algorithms","author":"Cormen","year":"2009"},{"key":"10.1016\/j.eswa.2026.133401_bib0014","series-title":"Proceedings of the 1996 ACM SIGMETRICS Conference","first-page":"160","article-title":"Self-similarity in world wide web traffic: Evidence and possible causes","author":"Crovella","year":"1997"},{"key":"10.1016\/j.eswa.2026.133401_bib0015","unstructured":"Dai, X., Wen, Q., Shen, Y., Wen, H., Li, D., Tang, J., & Shan, C. (2024). Revisiting the graph reasoning ability of large language models: Case studies in translation, connectivity and shortest path. 2408.09529."},{"key":"10.1016\/j.eswa.2026.133401_bib0016","unstructured":"DeepSeek AI (2025). Deepseek R1 distilled models. Available athttps:\/\/deepseek.com."},{"key":"10.1016\/j.eswa.2026.133401_bib0017","series-title":"Edsger wybe dijkstra: His life, work, and legacy","first-page":"287","article-title":"A note on two problems in connexion with graphs","author":"Dijkstra","year":"2022"},{"key":"10.1016\/j.eswa.2026.133401_bib0018","doi-asserted-by":"crossref","DOI":"10.1016\/j.jnca.2021.103215","article-title":"A QoS-based routing algorithm over software defined networks","volume":"194","author":"Elbasheer","year":"2021","journal-title":"Journal of Network and Computer Applications"},{"key":"10.1016\/j.eswa.2026.133401_bib0019","first-page":"17","article-title":"On the evolution of random graphs","volume":"5","author":"Erd\u0151s","year":"1960","journal-title":"Publications of the Mathematical Institute of the Hungarian Academy of Sciences"},{"key":"10.1016\/j.eswa.2026.133401_bib0020","series-title":"Statistical methods for research workers","author":"Fisher","year":"1992"},{"key":"10.1016\/j.eswa.2026.133401_bib0021","article-title":"Asymmetric lightweight cryptographic-based secure routing technique in iot-based WSN via optimal path selection using hybrid optimization algorithm","author":"Gnanaselvi","year":"2025","journal-title":"Knowledge-Based Systems"},{"key":"10.1016\/j.eswa.2026.133401_bib0022","series-title":"Introduction to probability","author":"Grinstead","year":"2012"},{"key":"10.1016\/j.eswa.2026.133401_sbref0020","series-title":"Exploring network structure, dynamics, and function using networkx","author":"Hagberg","year":"2008"},{"key":"10.1016\/j.eswa.2026.133401_bib0024","series-title":"Routing in the internet","author":"Huitema","year":"2000"},{"key":"10.1016\/j.eswa.2026.133401_bib0025","unstructured":"Jiang, A. et al. (2023). Mistral 7b. 2310.06825."},{"key":"10.1016\/j.eswa.2026.133401_bib0026","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.jnca.2016.04.003","article-title":"Energy-aware data center networks","volume":"68","author":"Jiang","year":"2016","journal-title":"Journal of Network and Computer Applications"},{"key":"10.1016\/j.eswa.2026.133401_bib0027","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.111661","article-title":"A two-stage method for doubly resource constrained elementary shortest path problems","volume":"293","author":"Jin","year":"2024","journal-title":"Knowledge-Based Systems"},{"key":"10.1016\/j.eswa.2026.133401_bib0028","series-title":"Uniform distribution of sequences","author":"Kuipers","year":"2012"},{"key":"10.1016\/j.eswa.2026.133401_bib0029","series-title":"Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling","first-page":"278","article-title":"Robust tests for equality of variances","author":"Levene","year":"1960"},{"issue":"6","key":"10.1016\/j.eswa.2026.133401_bib0030","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1016\/j.jnca.2012.07.021","article-title":"A systematic method for network topology reconfiguration with limited link additions","volume":"35","author":"Li","year":"2012","journal-title":"Journal of Network and Computer Applications"},{"issue":"5","key":"10.1016\/j.eswa.2026.133401_bib0031","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1641\/0006-3568(2001)051[0341:LNDATS]2.0.CO;2","article-title":"Log-normal distributions across the sciences: Keys and clues","volume":"51","author":"Limpert","year":"2001","journal-title":"BioScience"},{"key":"10.1016\/j.eswa.2026.133401_bib0032","article-title":"ARS: Adaptive routing strategies using at-gcn for traffic optimization in data center networks","author":"Liu","year":"2025","journal-title":"Journal of Network and Computer Applications"},{"key":"10.1016\/j.eswa.2026.133401_bib0033","unstructured":"Malkin, G. (1998). RIP version 2. RFC Editor. https:\/\/www.rfc-editor.org\/rfc\/rfc2453."},{"key":"10.1016\/j.eswa.2026.133401_bib0034","series-title":"ACM SIGCOMM Computer communication review","first-page":"18","article-title":"On the origin of power laws in internet topologies","volume":"vol. 30","author":"Medina","year":"2000"},{"key":"10.1016\/j.eswa.2026.133401_bib0035","series-title":"Proceedings IEEE 24th Annual joint conference of the IEEE Computer and communications societies","first-page":"2798","article-title":"A rational model for service rate allocation in peer-to-peer networks","volume":"vol. 4","author":"Meo","year":"2005"},{"key":"10.1016\/j.eswa.2026.133401_bib0036","unstructured":"Meta AI (2024). Meta AI: Llama 3.1 models. Available athttps:\/\/ai.meta.com\/research\/publications\/llama-3-1."},{"key":"10.1016\/j.eswa.2026.133401_bib0037","unstructured":"Moy, J. (1998). OSPF version 2. RFC Editor. https:\/\/www.rfc-editor.org\/rfc\/rfc2328."},{"key":"10.1016\/j.eswa.2026.133401_bib0038","unstructured":"OpenAI (2024). GPT-4o model card and benchmark results. Available athttps:\/\/docsbot.ai\/models\/gpt-4o."},{"key":"10.1016\/j.eswa.2026.133401_bib0039","unstructured":"OpenAI (2024). GPT-4o model card. Available athttps:\/\/openai.com\/index\/gpt-4o."},{"key":"10.1016\/j.eswa.2026.133401_bib0040","unstructured":"OpenAI (2025). Introducing GPT-5 for developers. Available athttps:\/\/openai.com\/index\/introducing-gpt-5-for-developers\/."},{"key":"10.1016\/j.eswa.2026.133401_bib0041","unstructured":"OpenAI (2025). Introducing GPT-5 for developers. Available athttps:\/\/openai.com\/index\/introducing-gpt-5-for-developers\/."},{"key":"10.1016\/j.eswa.2026.133401_bib0042","doi-asserted-by":"crossref","unstructured":"Rekhter, Y., Li, T., & Hares, S. (2006). A border gateway protocol 4 (BGP-4). RFC Editor. https:\/\/www.rfc-editor.org\/rfc\/rfc4271.","DOI":"10.17487\/rfc4271"},{"issue":"3","key":"10.1016\/j.eswa.2026.133401_bib0043","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1137\/0206041","article-title":"An analysis of several heuristics for the traveling salesman problem","volume":"6","author":"Rosenkrantz","year":"1977","journal-title":"SIAM Journal on Computing"},{"key":"10.1016\/j.eswa.2026.133401_bib0044","series-title":"Introduction to probability models","author":"Ross","year":"2014"},{"key":"10.1016\/j.eswa.2026.133401_bib0045","series-title":"9th USENIX Symposium on networked systems design and implementation (NSDI 12)","first-page":"225","article-title":"Jellyfish: Networking data centers randomly","author":"Singla","year":"2012"},{"key":"10.1016\/j.eswa.2026.133401_bib0046","unstructured":"Guide, T., (2025). ChatGPT-5 beats gemini and grok in tests \u2013 here\u2019s why that\u2019s important. Available athttps:\/\/www.tomsguide.com\/ai\/chatgpt-5-beats-gemini-and-grok-in-tests-heres-why-thats-important."},{"key":"10.1016\/j.eswa.2026.133401_bib0047","unstructured":"Touvron, H., Lavril, T., Izacard, G. et al. (2023). Llama: Open and efficient foundation language models. 2302.13971."},{"issue":"2","key":"10.1016\/j.eswa.2026.133401_bib0048","doi-asserted-by":"crossref","first-page":"99","DOI":"10.2307\/3001913","article-title":"Comparing individual means in the analysis of variance","volume":"5","author":"Tukey","year":"1949","journal-title":"Biometrics"},{"key":"10.1016\/j.eswa.2026.133401_bib0049","doi-asserted-by":"crossref","first-page":"30840","DOI":"10.52202\/075280-1345","article-title":"Can language models solve graph problems in natural language?","volume":"36","author":"Wang","year":"2023","journal-title":"Advances in Neural Information Processing Systems"},{"key":"10.1016\/j.eswa.2026.133401_bib0050","series-title":"Advances in neural information processing systems (neurIPS)","article-title":"Chain-of-thought prompting elicits reasoning in large language models","author":"Wei","year":"2022"},{"key":"10.1016\/j.eswa.2026.133401_bib0051","unstructured":"Wired (2025). Openai finally launched GPT-5. here\u2019s everything you need to know. Available athttps:\/\/www.wired.com\/story\/openais-gpt-5-is-here."},{"key":"10.1016\/j.eswa.2026.133401_bib0052","doi-asserted-by":"crossref","DOI":"10.1016\/j.jnca.2022.103542","article-title":"Flexible, highly scalable and cost-effective network structures for data centers","volume":"210","author":"Yu","year":"2023","journal-title":"Journal of Network and Computer Applications"},{"key":"10.1016\/j.eswa.2026.133401_sbref0038","article-title":"Extracting and following paths for robust relational reasoning with large language models","author":"Zhang","year":"2026","journal-title":"Transactions on Machine Learning Research"},{"key":"10.1016\/j.eswa.2026.133401_bib0054","series-title":"Proceedings of the 2000 ACM SIGCOMM conference","first-page":"197","article-title":"On the constancy of internet path properties","author":"Zhang","year":"2000"},{"issue":"1","key":"10.1016\/j.eswa.2026.133401_bib0055","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/COMST.2006.323440","article-title":"Routing in intermittently connected mobile ad hoc networks and delay tolerant networks: Overview and challenges","volume":"8","author":"Zhang","year":"2006","journal-title":"IEEE Communications Surveys & Tutorials"},{"key":"10.1016\/j.eswa.2026.133401_bib0056","series-title":"The eleventh international conference on learning representations (ICLR 2023)","article-title":"Automatic chain of thought prompting in large language models","author":"Zhang","year":"2023"}],"container-title":["Expert Systems with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426023109?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426023109?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T19:44:03Z","timestamp":1783021443000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0957417426023109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":56,"alternative-id":["S0957417426023109"],"URL":"https:\/\/doi.org\/10.1016\/j.eswa.2026.133401","relation":{},"ISSN":["0957-4174"],"issn-type":[{"value":"0957-4174","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Probing post-hoc reasoning in LLMs over multi-step pathfinding tasks","name":"articletitle","label":"Article Title"},{"value":"Expert Systems with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.eswa.2026.133401","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"133401"}}