Semi-Local Integration Measure of Node Importance
Numerous centrality measures have been introduced as tools to determine the importance of nodes in complex networks, reflecting various network properties, including connectivity, survivability, and robustness. In this paper, we introduce Semi-Local Integration (<inline-formula><math xmlns=...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/405 |
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| author | Tajana Ban Kirigin Sanda Bujačić Babić Benedikt Perak |
| author_facet | Tajana Ban Kirigin Sanda Bujačić Babić Benedikt Perak |
| author_sort | Tajana Ban Kirigin |
| collection | DOAJ |
| description | Numerous centrality measures have been introduced as tools to determine the importance of nodes in complex networks, reflecting various network properties, including connectivity, survivability, and robustness. In this paper, we introduce Semi-Local Integration (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi></mrow></semantics></math></inline-formula>), a node centrality measure for undirected and weighted graphs that takes into account the coherence of the locally connected subnetwork and evaluates the integration of nodes within their neighbourhood. We illustrate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi></mrow></semantics></math></inline-formula> node importance differentiation among nodes in lexical networks and demonstrate its potential in natural language processing (NLP). In the NLP task of sense identification and sense structure analysis, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula> centrality measure evaluates node integration and provides the necessary local resolution by differentiating the importance of nodes to a greater extent than standard centrality measures. This provides the relevant topological information about different subnetworks based on relatively local information, revealing the more complex sense structure. In addition, we show how the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula> measure can improve the results of sentiment analysis. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi></mrow></semantics></math></inline-formula> measure has the potential to be used in various types of complex networks in different research areas. |
| first_indexed | 2024-03-09T23:32:24Z |
| format | Article |
| id | doaj.art-ad4a13dd72e247348b9b464ff6f04296 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:32:24Z |
| publishDate | 2022-01-01 |
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| spelling | doaj.art-ad4a13dd72e247348b9b464ff6f042962023-11-23T17:06:57ZengMDPI AGMathematics2227-73902022-01-0110340510.3390/math10030405Semi-Local Integration Measure of Node ImportanceTajana Ban Kirigin0Sanda Bujačić Babić1Benedikt Perak2Department of Mathematics, University of Rijeka, R. Matejčić 2, 51000 Rijeka, CroatiaDepartment of Mathematics, University of Rijeka, R. Matejčić 2, 51000 Rijeka, CroatiaFaculty of Humanities and Social Sciences, University of Rijeka, Sveučilišna Avenija 4, 51000 Rijeka, CroatiaNumerous centrality measures have been introduced as tools to determine the importance of nodes in complex networks, reflecting various network properties, including connectivity, survivability, and robustness. In this paper, we introduce Semi-Local Integration (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi></mrow></semantics></math></inline-formula>), a node centrality measure for undirected and weighted graphs that takes into account the coherence of the locally connected subnetwork and evaluates the integration of nodes within their neighbourhood. We illustrate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi></mrow></semantics></math></inline-formula> node importance differentiation among nodes in lexical networks and demonstrate its potential in natural language processing (NLP). In the NLP task of sense identification and sense structure analysis, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula> centrality measure evaluates node integration and provides the necessary local resolution by differentiating the importance of nodes to a greater extent than standard centrality measures. This provides the relevant topological information about different subnetworks based on relatively local information, revealing the more complex sense structure. In addition, we show how the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula> measure can improve the results of sentiment analysis. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mi>I</mi></mrow></semantics></math></inline-formula> measure has the potential to be used in various types of complex networks in different research areas.https://www.mdpi.com/2227-7390/10/3/405centrality measurenode importancecomplex networksapplications of graph data processinglexical graph analysissentiment analysis |
| spellingShingle | Tajana Ban Kirigin Sanda Bujačić Babić Benedikt Perak Semi-Local Integration Measure of Node Importance Mathematics centrality measure node importance complex networks applications of graph data processing lexical graph analysis sentiment analysis |
| title | Semi-Local Integration Measure of Node Importance |
| title_full | Semi-Local Integration Measure of Node Importance |
| title_fullStr | Semi-Local Integration Measure of Node Importance |
| title_full_unstemmed | Semi-Local Integration Measure of Node Importance |
| title_short | Semi-Local Integration Measure of Node Importance |
| title_sort | semi local integration measure of node importance |
| topic | centrality measure node importance complex networks applications of graph data processing lexical graph analysis sentiment analysis |
| url | https://www.mdpi.com/2227-7390/10/3/405 |
| work_keys_str_mv | AT tajanabankirigin semilocalintegrationmeasureofnodeimportance AT sandabujacicbabic semilocalintegrationmeasureofnodeimportance AT benediktperak semilocalintegrationmeasureofnodeimportance |