Graphlet-based Self-Supervised Model for Topological Network Alignment

Graphlet-based Self-Supervised Model for Topological Network Alignment | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Graphlet-based Self-Supervised Model for Topological Network Alignment Mohammad Al Hasan, Abdullah Al Fahad, Aljohara Almulhim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7266987/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Network alignment aims to find the optimal nodes correspondences across twonetworks leveraging topological and/or attributes information. Existing methods of network alignment belong to two main categories: optimization-based methods and embedding-based methods. Optimization-based methods involvesolving eigen-decomposition of a similarity matrix, solving quadratic assignmentproblem via sub-gradient optimization, or using heuristic-based iterative greedymatch. Whereas the embedding-based methods utilize a cost function to learnnode representation vectors in a latent space followed by efficient node matching.Optimization based methods are more accurate but they are computationally expensive. Embedding-based methods generally exhibit the opposite trend. Inthis paper, we propose SST-Align, which solves the network alignment task byusing a hybrid approach. In the first stage of the hybrid method, SST-Align uses graphlet-count based topology signature of the vertices in an iterative greedymatching method for obtaining an initial alignment. Then in the second stage, theinitial alignment is used as self-supervised labels for learning node embedding by using a siamese neural network on top of graph convolutional networks. Extensive experiments conducted on six real-life graph alignment datasets demonstratethat our proposed method outperforms the current state-of-the-art graph align-ment methods in terms of node mapping accuracy. We then perform experiments on noisy datasets, built through random edge insertion; experimental results show that SST-Align suffers performance degradation in its second stage due to weak initial alignment in the first stage caused by the presence of noise, yet it achieves better alignment results than most other methods. Finally, we extend SST-Align for heterogeneous graphs by introducing a node-type induced tripletloss, and show experimental results on two heterogeneous networks. Self-Supervised Learning Graph Alignment Graphlets Features Topology-Based Matching Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 26 Nov, 2025 Reviews received at journal 17 Nov, 2025 Reviews received at journal 23 Oct, 2025 Reviewers agreed at journal 02 Oct, 2025 Reviewers agreed at journal 02 Oct, 2025 Reviewers agreed at journal 29 Sep, 2025 Reviewers invited by journal 27 Sep, 2025 Submission checks completed at journal 12 Sep, 2025 First submitted to journal 09 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7266987","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":525901813,"identity":"71d91ce0-ccab-485c-997e-0950b7d19504","order_by":0,"name":"Mohammad Al Hasan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVRIiWNgGAWjYDACdh4wJccGInmI0sIMUWZMupbEBqK18DfzHvz4o+ZOep9EAuODt21EaJE4zJcszXPsWW6bRAKz4VxitDAc5jGQZmA7DNLCJs1LjBb5wzzGP3/8O5zOJpHA/psoLQaHecwkeNsOJwC1sDETpcUQqMWat++wYRvPw2bJOeeI0CJ3vMf45o9vh+Xl25MPfnhTRoQWJMDYQJr6UTAKRsEoGAW4AQCtgS+m9reV3wAAAABJRU5ErkJggg==","orcid":"","institution":"Indiana University","correspondingAuthor":true,"prefix":"","firstName":"Mohammad","middleName":"Al","lastName":"Hasan","suffix":""},{"id":525901814,"identity":"5f54a008-b7cf-4efb-8a61-1ffdcf820241","order_by":1,"name":"Abdullah Al Fahad","email":"","orcid":"","institution":"Indiana University","correspondingAuthor":false,"prefix":"","firstName":"Abdullah","middleName":"Al","lastName":"Fahad","suffix":""},{"id":525901815,"identity":"66dd0d2a-08d0-47df-b666-fa41d36333e6","order_by":2,"name":"Aljohara Almulhim","email":"","orcid":"","institution":"Indiana University","correspondingAuthor":false,"prefix":"","firstName":"Aljohara","middleName":"","lastName":"Almulhim","suffix":""}],"badges":[],"createdAt":"2025-08-01 03:38:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7266987/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7266987/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93140427,"identity":"25fc46ec-ff41-40bb-bd6b-0e7cbd159108","added_by":"auto","created_at":"2025-10-09 12:57:44","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5866,"visible":true,"origin":"","legend":"","description":"","filename":"e6d3ac223ebf4c8a99f74d4b5e5d10c9.json","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/0b803685d810836aee15771d.json"},{"id":93139270,"identity":"58436894-7d84-4cd3-8e95-86f66d8985b6","added_by":"auto","created_at":"2025-10-09 12:49:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":66305,"visible":true,"origin":"","legend":"","description":"","filename":"Coverlettersst1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/2e6ac1c41f55fef571f1d1c7.pdf"},{"id":93140430,"identity":"2a8d1da5-fc1d-49e0-9de8-c5eb36064c0c","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":132920,"visible":true,"origin":"","legend":"","description":"","filename":"Coverlettersst.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/fad157d8cb6cac3e0f232839.pdf"},{"id":93139280,"identity":"fbf25376-53a9-4a1c-a150-ecf7960b8938","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":910844,"visible":true,"origin":"","legend":"","description":"","filename":"GraphAlignmentrevision1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/8e92fe44cd3d922be1505a8a.pdf"},{"id":93139278,"identity":"e779f787-e0d8-4329-8207-7c955cd370cf","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":32483,"visible":true,"origin":"","legend":"","description":"","filename":"Hit1accvs.Epoch40.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/ab21e6a77291349a4e8d6633.png"},{"id":93140429,"identity":"c24f451b-63f4-49a1-b8e8-2ca8cb3dd92a","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":42336,"visible":true,"origin":"","legend":"","description":"","filename":"corr.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/8205930214c37ec54b7e1f9c.png"},{"id":93139272,"identity":"dff931d9-37e9-4a3d-9669-0fd00a2ee030","added_by":"auto","created_at":"2025-10-09 12:49:44","extension":"eps","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2890,"visible":true,"origin":"","legend":"","description":"","filename":"empty.eps","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/dc22a0637a5bb6b8a8dfbf3f.eps"},{"id":93140428,"identity":"b8713fb2-aa2a-47a9-99f1-3675eff1b4e1","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"eps","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":91593,"visible":true,"origin":"","legend":"","description":"","filename":"fig.eps","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/ef1ff4992949ac651d2f4683.eps"},{"id":93140431,"identity":"d2d72371-000c-4a23-aa0b-bf17e775a933","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":112004,"visible":true,"origin":"","legend":"","description":"","filename":"fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/4785cec4c0490e1eec3e7ceb.png"},{"id":93139274,"identity":"0b96e7c6-84ec-40a5-957b-9765eee83a7a","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":75519,"visible":true,"origin":"","legend":"","description":"","filename":"fig2fixed.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/3996cd38b1f24307dd4e612c.png"},{"id":93139273,"identity":"c5d2a4c3-e0a6-4481-8e67-1ffb47b255e0","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":33963,"visible":true,"origin":"","legend":"","description":"","filename":"gamma.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/be3d3b45f350e28e716af662.png"},{"id":93142597,"identity":"bd026019-f0cc-4656-b417-c595a7a4d631","added_by":"auto","created_at":"2025-10-09 13:13:45","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":170440,"visible":true,"origin":"","legend":"","description":"","filename":"graphlet.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/1480a76c0ec1f76a8f11182a.png"},{"id":93140440,"identity":"fcad80b8-2135-4d1b-a99d-b44250ab0282","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":94906,"visible":true,"origin":"","legend":"","description":"","filename":"lossaccsparse.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/8b4d5deace98cc22e5b5c504.png"},{"id":93139292,"identity":"0f680be5-4e3e-4e11-bd32-30ca9cb695df","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":32021,"visible":true,"origin":"","legend":"","description":"","filename":"losscurve.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/833d02638f52c0b7cf977637.png"},{"id":93143430,"identity":"69c21195-d633-48b1-af4a-fe1674b8e390","added_by":"auto","created_at":"2025-10-09 13:21:45","extension":"bst","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":146013,"visible":true,"origin":"","legend":"","description":"","filename":"snapacite.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/a615921d0de996e7fc9996bb.bst"},{"id":93140436,"identity":"c2516ae5-514f-4567-acd4-6c22d981d649","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"bst","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29828,"visible":true,"origin":"","legend":"","description":"","filename":"snaps.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/30ce021c9901c9164a2b99b7.bst"},{"id":93139285,"identity":"84ccfd07-b363-4152-976d-d66368e712b5","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"pdf","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":421391,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/6da7311d7c28abb3c6d78c09.pdf"},{"id":93141103,"identity":"65679ae8-e398-441a-b7c5-23d9f014f5ee","added_by":"auto","created_at":"2025-10-09 13:05:45","extension":"bst","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":35515,"visible":true,"origin":"","legend":"","description":"","filename":"snbasic.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/16c926fc4cd46c91ce35d391.bst"},{"id":93139281,"identity":"55bdf1f2-f66b-41a7-a474-71d3c6175a17","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"bst","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":33968,"visible":true,"origin":"","legend":"","description":"","filename":"snchicago.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/de16c62c1b41488dcd889fc0.bst"},{"id":93140433,"identity":"76cf905b-7aa3-4623-8b21-a3426144ca64","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"cls","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":55857,"visible":true,"origin":"","legend":"","description":"","filename":"snjnl.cls","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/055f6f7b5222a0903ee023c6.cls"},{"id":93139288,"identity":"c06f5d53-3dca-462e-9200-71bbd02f9afe","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"bst","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64023,"visible":true,"origin":"","legend":"","description":"","filename":"snmathphysay.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/76c47f966dca576a0ab3cc16.bst"},{"id":93141104,"identity":"2a943440-b067-4269-8ea4-da88880b55a7","added_by":"auto","created_at":"2025-10-09 13:05:45","extension":"bst","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64166,"visible":true,"origin":"","legend":"","description":"","filename":"snmathphysnum.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/b5c358ba42c3283b22730b31.bst"},{"id":93140435,"identity":"9966faaa-90a1-475e-aec5-b29bb51df184","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"bst","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":37333,"visible":true,"origin":"","legend":"","description":"","filename":"snnature.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/76003bd95efaaebb79aab992.bst"},{"id":93139283,"identity":"86d2e46a-e1ff-4b6d-b7bf-48b3a2e85f17","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"bst","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":39951,"visible":true,"origin":"","legend":"","description":"","filename":"snvancouveray.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/29952faaaed478dd6c5c9f6a.bst"},{"id":93139300,"identity":"cdf782d4-5407-457f-aa94-326aaa69d113","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"bst","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":40758,"visible":true,"origin":"","legend":"","description":"","filename":"snvancouvernum.bst","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/40af7ecbf4f5fcb36f329e5c.bst"},{"id":93139303,"identity":"451607b6-8336-4008-8ca2-1ab928fb902e","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"pdf","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":418495,"visible":true,"origin":"","legend":"","description":"","filename":"usermanual.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/be6054359f610e36d9077d3c.pdf"},{"id":93139294,"identity":"4dd66e17-e17b-4a67-849d-9ff6172c9bec","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":42989,"visible":true,"origin":"","legend":"","description":"","filename":"zacharyplot.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/ac4f61eeeb2803825171e051.png"},{"id":93140441,"identity":"b96fd531-8cf8-4fb9-a9b2-977c21388012","added_by":"auto","created_at":"2025-10-09 12:57:45","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":26931,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineHit1accvs.Epoch40.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/e5066988f8f90724532ab17b.png"},{"id":93139295,"identity":"1ac0f814-ff05-49fc-8a48-fdfc59011d30","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":34958,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinecorr.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/c9a93f383264370620f95b12.png"},{"id":93139302,"identity":"9a445637-0abd-45a8-9483-00ee7c2f4769","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":101367,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefig1.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/7bf5073c2044fb701b5a7ff8.png"},{"id":93139297,"identity":"b7d81e32-4cf3-4b40-b13e-8704fd392332","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":69303,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefig2fixed.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/2b52f3f21bbfddbcdca9f114.png"},{"id":93139298,"identity":"ea7456ea-7526-4a9f-a0bd-68d74c8942e6","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":28778,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinegamma.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/421867c33146c4e4f482730e.png"},{"id":93139304,"identity":"780faecc-8888-4868-92a5-97a1f92110eb","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":159656,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinegraphlet.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/d0d3fe701a44fb08a5834a05.png"},{"id":93139307,"identity":"3b8809b1-11fc-48ce-bad4-ab04aa06a5d1","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":80504,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinelossaccsparse.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/1b34fc19b9697bc49e6db25a.png"},{"id":93139301,"identity":"8ada84ff-07e2-452e-bc03-3a16c839ca7f","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":27500,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinelosscurve.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/2c8978687c791ba8bf202230.png"},{"id":93139305,"identity":"19df5187-451a-4ecd-9ca6-9cc5f391a960","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"png","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":40689,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinezacharyplot.png","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/49cf5d98a395e3c54cbe3799.png"},{"id":93139299,"identity":"828015ac-6684-4936-93f0-e204961df1f2","added_by":"auto","created_at":"2025-10-09 12:49:45","extension":"xml","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":147390,"visible":true,"origin":"","legend":"","description":"","filename":"e6d3ac223ebf4c8a99f74d4b5e5d10c91structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1/b068f4ea06848d064b194889.xml"},{"id":93225285,"identity":"0d15e6ed-3c6c-4873-bb72-4f536869a5e5","added_by":"auto","created_at":"2025-10-10 12:20:07","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":754221,"visible":true,"origin":"","legend":"","description":"","filename":"GraphAlignmentrevision1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7266987/v1_covered_f521c4f5-3fcb-4a39-a940-5633fe165b24.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Graphlet-based Self-Supervised Model for Topological Network Alignment","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"applied-network-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apns","sideBox":"Learn more about [Applied Network Science](http://appliednetsci.springeropen.com/)","snPcode":"41109","submissionUrl":"https://submission.nature.com/new-submission/41109/3","title":"Applied Network Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Self-Supervised Learning, Graph Alignment, Graphlets Features, Topology-Based Matching","lastPublishedDoi":"10.21203/rs.3.rs-7266987/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7266987/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Network alignment aims to find the optimal nodes correspondences across twonetworks leveraging topological and/or attributes information. Existing methods of network alignment belong to two main categories: optimization-based methods and embedding-based methods. Optimization-based methods involvesolving eigen-decomposition of a similarity matrix, solving quadratic assignmentproblem via sub-gradient optimization, or using heuristic-based iterative greedymatch. Whereas the embedding-based methods utilize a cost function to learnnode representation vectors in a latent space followed by efficient node matching.Optimization based methods are more accurate but they are computationally expensive. Embedding-based methods generally exhibit the opposite trend. Inthis paper, we propose SST-Align, which solves the network alignment task byusing a hybrid approach. In the first stage of the hybrid method, SST-Align uses graphlet-count based topology signature of the vertices in an iterative greedymatching method for obtaining an initial alignment. Then in the second stage, theinitial alignment is used as self-supervised labels for learning node embedding by using a siamese neural network on top of graph convolutional networks. Extensive experiments conducted on six real-life graph alignment datasets demonstratethat our proposed method outperforms the current state-of-the-art graph align-ment methods in terms of node mapping accuracy. We then perform experiments on noisy datasets, built through random edge insertion; experimental results show that SST-Align suffers performance degradation in its second stage due to weak initial alignment in the first stage caused by the presence of noise, yet it achieves better alignment results than most other methods. Finally, we extend SST-Align for heterogeneous graphs by introducing a node-type induced tripletloss, and show experimental results on two heterogeneous networks.","manuscriptTitle":"Graphlet-based Self-Supervised Model for Topological Network Alignment","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-09 12:49:40","doi":"10.21203/rs.3.rs-7266987/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-27T02:55:45+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-17T10:38:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-24T03:33:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"93019973546067628028452813208144130005","date":"2025-10-03T00:36:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87444460706107759529721910967597591860","date":"2025-10-02T10:46:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"170883181067073233954218862941663867993","date":"2025-09-29T10:16:48+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-27T10:38:06+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-12T07:49:32+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Network Science","date":"2025-09-10T03:14:56+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-network-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apns","sideBox":"Learn more about [Applied Network Science](http://appliednetsci.springeropen.com/)","snPcode":"41109","submissionUrl":"https://submission.nature.com/new-submission/41109/3","title":"Applied Network Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"088867dc-d453-418f-93bc-0b99e7280d59","owner":[],"postedDate":"October 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-01-28T14:25:27+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-09 12:49:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7266987","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7266987","identity":"rs-7266987","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}