Centrality measures for node-weighted networks via line graphs and the matrix exponential
This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted n...
Gespeichert in:
| Veröffentlicht in: | Numerical algorithms 2021-10, Vol.88 (2), p.583-614 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 614 |
|---|---|
| container_issue | 2 |
| container_start_page | 583 |
| container_title | Numerical algorithms |
| container_volume | 88 |
| creator | De la Cruz Cabrera, Omar Matar, Mona Reichel, Lothar |
| description | This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted networks. However, adjacency matrices for node-weighted graphs have not received much attention. The present paper proposes using a line graph associated with a node-weighted graph to construct an edge-weighted graph that can be analyzed with available methods. Both undirected and directed graphs with positive node weights are considered. We show that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled. Applications to real-life problems are presented. |
| doi_str_mv | 10.1007/s11075-020-01050-0 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2918491141</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2918491141</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-b691a5fcd0ca20a575ab17b1423e45953283e1ad7842acce5df67fb0d6b6fb483</originalsourceid><addsrcrecordid>eNp9kD1PwzAQhi0EEqXwB5gsMQfunDhORlTxJVVigYHJcpJLm5I6xXZp--8xBImN5e6G531Pehi7RLhGAHXjEUHJBAQkgCDjPGITlEokpcjlcbwBVYJpWZyyM-9XECkQasLeZmSDM30XDnxNxm8ded4OjtuhoWRH3WIZqOGWwm5w755_dob3nSW-cGaz9NzYhocl8bUJrttz2m8GGxs705-zk9b0ni5-95S93t-9zB6T-fPD0-x2ntQpliGp8hKNbOsGaiPASCVNharCTKSUyVKmokgJTaOKTJi6Jtm0uWoraPIqb6usSKfsauzduOFjSz7o1bB1Nr7UosQiKxEzjJQYqdoN3jtq9cZ1a-MOGkF_K9SjQh0V6h-FGmIoHUM-wnZB7q_6n9QXtoV1Fg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2918491141</pqid></control><display><type>article</type><title>Centrality measures for node-weighted networks via line graphs and the matrix exponential</title><source>SpringerLink Journals - AutoHoldings</source><creator>De la Cruz Cabrera, Omar ; Matar, Mona ; Reichel, Lothar</creator><creatorcontrib>De la Cruz Cabrera, Omar ; Matar, Mona ; Reichel, Lothar</creatorcontrib><description>This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted networks. However, adjacency matrices for node-weighted graphs have not received much attention. The present paper proposes using a line graph associated with a node-weighted graph to construct an edge-weighted graph that can be analyzed with available methods. Both undirected and directed graphs with positive node weights are considered. We show that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled. Applications to real-life problems are presented.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-020-01050-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Computer Science ; Graph theory ; Graphs ; Linear algebra ; Nodes ; Numeric Computing ; Numerical Analysis ; Original Paper ; Theory of Computation</subject><ispartof>Numerical algorithms, 2021-10, Vol.88 (2), p.583-614</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-b691a5fcd0ca20a575ab17b1423e45953283e1ad7842acce5df67fb0d6b6fb483</citedby><cites>FETCH-LOGICAL-c319t-b691a5fcd0ca20a575ab17b1423e45953283e1ad7842acce5df67fb0d6b6fb483</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11075-020-01050-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11075-020-01050-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>De la Cruz Cabrera, Omar</creatorcontrib><creatorcontrib>Matar, Mona</creatorcontrib><creatorcontrib>Reichel, Lothar</creatorcontrib><title>Centrality measures for node-weighted networks via line graphs and the matrix exponential</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><description>This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted networks. However, adjacency matrices for node-weighted graphs have not received much attention. The present paper proposes using a line graph associated with a node-weighted graph to construct an edge-weighted graph that can be analyzed with available methods. Both undirected and directed graphs with positive node weights are considered. We show that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled. Applications to real-life problems are presented.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computer Science</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Linear algebra</subject><subject>Nodes</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Theory of Computation</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9kD1PwzAQhi0EEqXwB5gsMQfunDhORlTxJVVigYHJcpJLm5I6xXZp--8xBImN5e6G531Pehi7RLhGAHXjEUHJBAQkgCDjPGITlEokpcjlcbwBVYJpWZyyM-9XECkQasLeZmSDM30XDnxNxm8ded4OjtuhoWRH3WIZqOGWwm5w755_dob3nSW-cGaz9NzYhocl8bUJrttz2m8GGxs705-zk9b0ni5-95S93t-9zB6T-fPD0-x2ntQpliGp8hKNbOsGaiPASCVNharCTKSUyVKmokgJTaOKTJi6Jtm0uWoraPIqb6usSKfsauzduOFjSz7o1bB1Nr7UosQiKxEzjJQYqdoN3jtq9cZ1a-MOGkF_K9SjQh0V6h-FGmIoHUM-wnZB7q_6n9QXtoV1Fg</recordid><startdate>20211001</startdate><enddate>20211001</enddate><creator>De la Cruz Cabrera, Omar</creator><creator>Matar, Mona</creator><creator>Reichel, Lothar</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20211001</creationdate><title>Centrality measures for node-weighted networks via line graphs and the matrix exponential</title><author>De la Cruz Cabrera, Omar ; Matar, Mona ; Reichel, Lothar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-b691a5fcd0ca20a575ab17b1423e45953283e1ad7842acce5df67fb0d6b6fb483</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Computer Science</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Linear algebra</topic><topic>Nodes</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>De la Cruz Cabrera, Omar</creatorcontrib><creatorcontrib>Matar, Mona</creatorcontrib><creatorcontrib>Reichel, Lothar</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>De la Cruz Cabrera, Omar</au><au>Matar, Mona</au><au>Reichel, Lothar</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Centrality measures for node-weighted networks via line graphs and the matrix exponential</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2021-10-01</date><risdate>2021</risdate><volume>88</volume><issue>2</issue><spage>583</spage><epage>614</epage><pages>583-614</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted networks. However, adjacency matrices for node-weighted graphs have not received much attention. The present paper proposes using a line graph associated with a node-weighted graph to construct an edge-weighted graph that can be analyzed with available methods. Both undirected and directed graphs with positive node weights are considered. We show that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled. Applications to real-life problems are presented.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11075-020-01050-0</doi><tpages>32</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1017-1398 |
| ispartof | Numerical algorithms, 2021-10, Vol.88 (2), p.583-614 |
| issn | 1017-1398 1572-9265 |
| language | eng |
| recordid | cdi_proquest_journals_2918491141 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Algorithms Computer Science Graph theory Graphs Linear algebra Nodes Numeric Computing Numerical Analysis Original Paper Theory of Computation |
| title | Centrality measures for node-weighted networks via line graphs and the matrix exponential |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-08T02%3A23%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Centrality%20measures%20for%20node-weighted%20networks%20via%20line%20graphs%20and%20the%20matrix%20exponential&rft.jtitle=Numerical%20algorithms&rft.au=De%20la%20Cruz%20Cabrera,%20Omar&rft.date=2021-10-01&rft.volume=88&rft.issue=2&rft.spage=583&rft.epage=614&rft.pages=583-614&rft.issn=1017-1398&rft.eissn=1572-9265&rft_id=info:doi/10.1007/s11075-020-01050-0&rft_dat=%3Cproquest_cross%3E2918491141%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2918491141&rft_id=info:pmid/&rfr_iscdi=true |