{"id":"https://openalex.org/W7224119384","doi":"https://doi.org/10.48550/arxiv.2610.37580","title":"Spectral Braids: A Topological Descriptor for Dynamic Directed Networks","display_name":"Spectral Braids: A Topological Descriptor for Dynamic Directed Networks","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224119384","doi":"https://doi.org/10.48550/arxiv.2610.37580"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37580","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37580","pdf_url":"https://arxiv.org/pdf/2610.37580","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.37580","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076725374","display_name":"Mehmet Emin Aktas","orcid":"https://orcid.org/0000-0002-9527-9600","observed_orcids":["https://orcid.org/0000-0002-9527-9600","https://orcid.org/0009-0008-8052-9866"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aktas, Mehmet Emin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080080406","display_name":"Esra Akba\u015f","orcid":"https://orcid.org/0000-0002-8817-2442","observed_orcids":["https://orcid.org/0000-0002-8817-2442"]},"institutions":[{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Akbas, Esra","raw_affiliation_strings":["Department of Computer Science Georgia State University Atlanta , GA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science Georgia State University Atlanta , GA , USA","institution_ids":["https://openalex.org/I181565077"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.29030001163482666,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.29030001163482666,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.24500000476837158,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.20810000598430634,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/complex-eigenvalues","display_name":"complex eigenvalues","score":0.7590000033378601},{"id":"https://openalex.org/keywords/braid-monodromy","display_name":"braid monodromy","score":0.9440000057220459},{"id":"https://openalex.org/keywords/burau-representation","display_name":"Burau representation","score":0.9929999709129333},{"id":"https://openalex.org/keywords/topological-properties","display_name":"topological properties","score":0.5580000281333923},{"id":"https://openalex.org/keywords/online-communities","display_name":"online communities","score":0.75},{"id":"https://openalex.org/keywords/graph-learning","display_name":"graph learning","score":0.43299999833106995}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6933000087738037},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.6247000098228455},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.621399998664856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48249998688697815},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.43320000171661377},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.398499995470047},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3955000042915344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3919000029563904},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33149999380111694},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C2780311589","wikidata":"https://www.wikidata.org/wiki/Q6901559","display_name":"Monodromy matrix","level":3,"score":0.32100000977516174},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.28679999709129333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2822999954223633},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C28940832","wikidata":"https://www.wikidata.org/wiki/Q3490774","display_name":"Spectrum of a matrix","level":4,"score":0.2628999948501587}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.37580","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37580","pdf_url":"https://arxiv.org/pdf/2610.37580","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.37580","doi":"https://doi.org/10.48550/arxiv.2610.37580","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37580","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.37580","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37580","pdf_url":"https://arxiv.org/pdf/2610.37580","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224119384.pdf","grobid_xml":"https://content.openalex.org/works/W7224119384.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2619577565","https://openalex.org/W4394668956","https://openalex.org/W7135686026","https://openalex.org/W2399091303","https://openalex.org/W7139367566","https://openalex.org/W4309009361","https://openalex.org/W7207689913","https://openalex.org/W2539308428","https://openalex.org/W2899042395","https://openalex.org/W3087852383"],"abstract_inverted_index":{"Eigenvalues":[0],"are":[1,29,102],"a":[2,19,25,34,40,73,75,84,95,115,123,131,141,148,228],"workhorse":[3],"of":[4,24,37,69,150,172,234,241],"graph":[5,11,15,41,256],"machine":[6],"learning:":[7],"spectral":[8,10,82],"clustering,":[9],"neural":[12],"networks,":[13],"and":[14,47,106,153,186,215,252,258],"kernels":[16],"all":[17],"summarize":[18],"network":[20,167,180],"by":[21,125],"the":[22,49,57,107,126,163,179,183,194,206,217,224,239,246],"eigenvalues":[23,28,45,101],"matrix.":[26],"These":[27],"almost":[30],"always":[31],"treated":[32],"as":[33,114,261],"static":[35],"list":[36],"numbers.":[38],"When":[39],"changes,":[42],"however,":[43],"its":[44,99],"move,":[46],"when":[48],"matrix":[50,124],"is":[51,72,92,111,119,245],"not":[52,212],"symmetric,":[53],"they":[54,61,109],"move":[55],"in":[56,227],"complex":[58,100],"plane,":[59],"where":[60],"can":[62],"wind":[63],"around":[64],"each":[65,90,144,154],"other.":[66],"The":[67,117,138],"pattern":[68],"this":[70,244],"winding":[71],"braid,":[74],"classical":[76],"object":[77],"from":[78],"topology.":[79],"We":[80,161],"propose":[81],"braids,":[83],"methodology":[85],"for":[86,135,205,263],"dynamic":[87,166,266],"directed":[88],"networks:":[89],"snapshot":[91],"aggregated":[93],"into":[94],"community-level":[96],"transition":[97],"matrix,":[98],"tracked":[103],"over":[104],"time,":[105],"braid":[108,139,253],"trace":[110],"read":[112],"off":[113],"word.":[116],"word":[118],"then":[120],"mapped":[121],"to":[122],"Burau":[127,218],"representation,":[128],"which":[129,231],"gives":[130],"fixed-size":[132],"feature":[133,208],"vector":[134],"any":[136],"classifier.":[137],"has":[140],"concrete":[142],"meaning:":[143],"eigenvalue":[145],"describes":[146],"how":[147,178],"group":[149,158],"communities":[151,174],"behaves,":[152],"crossing":[155],"records":[156],"one":[157],"overtaking":[159],"another.":[160],"evaluate":[162],"method":[164],"on":[165,200,255,265],"classification,":[168],"using":[169],"synthetic":[170],"networks":[171,222],"online":[173],"whose":[175],"labels":[176],"describe":[177],"evolved":[181],"between":[182],"same":[184,225],"starting":[185],"ending":[187],"states.":[188],"Our":[189],"experimental":[190],"results":[191],"show":[192],"that":[193,210,216,249],"proposed":[195],"features":[196,219,262],"reach":[197],"97.1%":[198],"accuracy":[199],"four":[201],"classes,":[202],"against":[203],"44.5%":[204],"best":[207,240],"set":[209],"does":[211],"track":[213],"eigenvalues,":[214],"also":[220],"separate":[221],"containing":[223],"events":[226],"different":[229],"order,":[230],"simple":[232],"counts":[233],"crossings":[235],"cannot":[236],"do.":[237],"To":[238],"our":[242],"knowledge,":[243],"first":[247],"study":[248],"defines":[250],"braids":[251],"monodromy":[254],"data":[257],"uses":[259],"them":[260],"learning":[264],"networks.":[267]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-29T00:00:00"}