{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/107975"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/107975","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Graph connectivity and vector degree in motif-based graphs","abstract":"Graph theory is frequently used to model and encode relationships in social networks, the internet, or biology. Due to the fundamental limitation that an edge can only connect two nodes, a standard graph is only capable of describing pairwise relationships. Therefore, some new models have been introduced to capture the relationships among more than two nodes by replacing standard edges with novel representations, like motif-edge or hyperedge. By replacing standard edges with motif-edges, the graph succeeds in describing the higher-order complex networks. However, a problem of connectivity in motif-based graphs also arises because generated motif-based graphs can be disconnected even though the standard graphs are connected. Here we first survey existing works on connectivity metrics in standard graphs, then propose a new measurement of degree, called vector degree, to extend the definition of degree from standard graphs to motif-based graphs. Some properties of vector degree will be compared with standard degree, and some connectivity metrics will be extended to motif-based graphs as well.","abstract_html":"Graph theory is frequently used to model and encode relationships in social networks, the internet, or biology. Due to the fundamental limitation that an edge can only connect two nodes, a standard graph is only capable of describing pairwise relationships. Therefore, some new models have been introduced to capture the relationships among more than two nodes by replacing standard edges with novel representations, like motif-edge or hyperedge. By replacing standard edges with motif-edges, the graph succeeds in describing the higher-order complex networks. However, a problem of connectivity in motif-based graphs also arises because generated motif-based graphs can be disconnected even though the standard graphs are connected. Here we first survey existing works on connectivity metrics in standard graphs, then propose a new measurement of degree, called vector degree, to extend the definition of degree from standard graphs to motif-based graphs. Some properties of vector degree will be compared with standard degree, and some connectivity metrics will be extended to motif-based graphs as well.","abstract_has_math":false,"creators":["Wang, Qihao"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Chang, Kevin Chen-Chuan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-26T21:54:49Z","date_published":"2020-08-26T21:54:49Z","updated_at":"2026-07-22T22:24:47Z","subjects":["data mining","degree","graph theory"],"languages":["en"],"rights":["Copyright 2020 Qihao Wang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/107975","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chang, Kevin Chen-Chuan"]},{"key":"dc:creator","label":"Author","values":["Wang, Qihao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-26T21:54:49Z","2020-05-10","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["data mining","degree","graph theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Qihao Wang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/107975"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Graph theory is frequently used to model and encode relationships in social networks, the internet, or biology. Due to the fundamental limitation that an edge can only connect two nodes, a standard graph is only capable of describing pairwise relationships. Therefore, some new models have been introduced to capture the relationships among more than two nodes by replacing standard edges with novel representations, like motif-edge or hyperedge. By replacing standard edges with motif-edges, the graph succeeds in describing the higher-order complex networks. However, a problem of connectivity in motif-based graphs also arises because generated motif-based graphs can be disconnected even though the standard graphs are connected. Here we first survey existing works on connectivity metrics in standard graphs, then propose a new measurement of degree, called vector degree, to extend the definition of degree from standard graphs to motif-based graphs. Some properties of vector degree will be compared with standard degree, and some connectivity metrics will be extended to motif-based graphs as well.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, Qihao Wang, accepted the attached license on 2020-05-04 at 08:52.","The student, Qihao Wang, submitted this Thesis for approval on 2020-05-04 at 08:52.","This Thesis was approved for publication on 2020-05-10 at 15:41.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15183 on 2020-08-25 at 17:11:35","Made available in DSpace on 2020-08-26T21:54:49Z (GMT). No. of bitstreams: 2 WANG-THESIS-2020.pdf: 288795 bytes, checksum: ccd9186061a1cc189b7c927a0c82a834 (MD5) LICENSE.txt: 4207 bytes, checksum: 15db83fd2452e9ef5407b203ffe02973 (MD5) Previous issue date: 2020-05-10"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Graph connectivity and vector degree in motif-based graphs"]}]}],"canonical_facts":{"dc:contributor":["Chang, Kevin Chen-Chuan"],"dc:creator":["Wang, Qihao"],"dc:date":["2020-08-26T21:54:49Z","2020-05-10","2020-05"],"dc:description":["Graph theory is frequently used to model and encode relationships in social networks, the internet, or biology. Due to the fundamental limitation that an edge can only connect two nodes, a standard graph is only capable of describing pairwise relationships. Therefore, some new models have been introduced to capture the relationships among more than two nodes by replacing standard edges with novel representations, like motif-edge or hyperedge. By replacing standard edges with motif-edges, the graph succeeds in describing the higher-order complex networks. However, a problem of connectivity in motif-based graphs also arises because generated motif-based graphs can be disconnected even though the standard graphs are connected. Here we first survey existing works on connectivity metrics in standard graphs, then propose a new measurement of degree, called vector degree, to extend the definition of degree from standard graphs to motif-based graphs. Some properties of vector degree will be compared with standard degree, and some connectivity metrics will be extended to motif-based graphs as well.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, Qihao Wang, accepted the attached license on 2020-05-04 at 08:52.","The student, Qihao Wang, submitted this Thesis for approval on 2020-05-04 at 08:52.","This Thesis was approved for publication on 2020-05-10 at 15:41.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15183 on 2020-08-25 at 17:11:35","Made available in DSpace on 2020-08-26T21:54:49Z (GMT). No. of bitstreams: 2 WANG-THESIS-2020.pdf: 288795 bytes, checksum: ccd9186061a1cc189b7c927a0c82a834 (MD5) LICENSE.txt: 4207 bytes, checksum: 15db83fd2452e9ef5407b203ffe02973 (MD5) Previous issue date: 2020-05-10"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/107975"],"dc:language":["en"],"dc:rights":["Copyright 2020 Qihao Wang"],"dc:subject":["data mining","degree","graph theory"],"dc:title":["Graph connectivity and vector degree in motif-based graphs"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:47Z"}