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On centrality functions of a graph [chapter]

G. Kishi
1981 Lecture Notes in Computer Science  
For a weakly connected directed graph, we can prove similar theorems with respect to a generalized centrality function based on a new definition of the modified distance from a vertex to another vertex  ...  For a connected nondirected graph, a centrality function is a real valued function of the vertices defined as a linear combination of the numbers of the vertices classified according to the distance from  ...  One of the most important problems is to determine what kind of functions is suitable for the measure of centrality of vertices in a graph.  ... 
doi:10.1007/3-540-10704-5_5 fatcat:gjknohulczasdpbjjga7nau5hy

Structure Can Predict Function in the Human Brain: A Graph Neural Network Deep Learning Model of Functional Connectivity and Centrality based on Structural Connectivity [article]

Josh Neudorf, Shaylyn Kress, Ron Borowsky
2021 bioRxiv   pre-print
Although functional connectivity and associated graph theory measures (e.g., centrality; how centrally important to the network a region is) are widely used in brain research, the full extent to which  ...  , and 91% of the variance in functional centrality.  ...  Still, there remains a large amount of 62 variance unaccounted for if we are to determine the extent to which functional connectivity and 63 measures of centrality based on functional connectivity offer  ... 
doi:10.1101/2021.03.15.435531 fatcat:xbo5f4s5tjczzdaagwtnppbe2y

Cost-constrained and centrality-balanced network design improvement

Mohammed J.F. Alenazi, Egemen K. Cetinkaya, James P.G. Sterbenz
2014 2014 6th International Workshop on Reliable Networks Design and Modeling (RNDM)  
We develop a heuristic algorithm that balances the centrality of networks by adding a set of links that minimizes the variance of graph centrality measures in a least costly fashion.  ...  We apply our algorithm to three different realistic topologies and measure the performance of the improved graphs in terms of flow robustness when subjected to targeted attacks.  ...  ACKNOWLEDGMENTS We would like to acknowledge Dongsheng Zhang for discussions on this work.  ... 
doi:10.1109/rndm.2014.7014951 fatcat:ku6oy7rwczf7bk7s2otiddsk4a

The Effects of Centrality Ordering in Label Propagation for Community Detection

Brian Dickinson, Wei Hu
2015 Social Networking  
The results of testing seven various measures of centrality in conjunction with SLPA across five social network graphs indicate that while certain measures outperform random orderings on certain graphs  ...  This study evaluates the effects of such orderings on the Speaker-listener Label Propagation Algorithm or SLPA, a modification of LPA which has already been stabilized through alternate means.  ...  Community Partitioning Quality of SLPA Using Various Centrality Measures Each centrality function was used in running SLPA one-hundred times on each graph.  ... 
doi:10.4236/sn.2015.44012 fatcat:sua4hhd52zfepnwoe446qchin4

Analysis of function-call graphs of open-source software systems using complex network analysis

Volkan Tunalı, Mehmet Ali Aksoy Tüysüz
2020 Pamukkale University Journal of Engineering Sciences  
In addition, we identified the most central and important functions in each call-graph using several centrality measures.  ...  Öz Software systems are usually designed in a modular and hierarchical fashion, where functional responsibility of a system is decomposed into multiple functional software elements optimally such as subsystems  ...  The higher the centrality value, the more central a node is. In-degree of a node (function) in call graphs is the number of other functions that directly call this function, also known as fan-in.  ... 
doi:10.5505/pajes.2019.63239 fatcat:wu4g7lafb5dixgn4bxoe7ki7za

Active learning for protein function prediction in protein–protein interaction networks

Wei Xiong, Luyu Xie, Shuigeng Zhou, Jihong Guan
2014 Neurocomputing  
The high-throughput technologies have led to vast amounts of protein-protein interaction (PPI) data, and a number of approaches based on PPI networks have been proposed for protein function prediction.  ...  protein function based on these annotated proteins.  ...  Jihong Guan was also supported by the "Shuguang Scholar" Program of Shanghai Education Foundation.  ... 
doi:10.1016/j.neucom.2014.05.075 fatcat:icapxq5firbv7m66psbwxrctdy

Active Learning for Protein Function Prediction in Protein-Protein Interaction Networks [chapter]

Wei Xiong, Luyu Xie, Jihong Guan, Shuigeng Zhou
2013 Lecture Notes in Computer Science  
The high-throughput technologies have led to vast amounts of protein-protein interaction (PPI) data, and a number of approaches based on PPI networks have been proposed for protein function prediction.  ...  protein function based on these annotated proteins.  ...  Jihong Guan was also supported by the "Shuguang Scholar" Program of Shanghai Education Foundation.  ... 
doi:10.1007/978-3-642-39159-0_16 fatcat:rpjujkaernclvfti6is2yzwcay

Path Evaluation and Centralities in Weighted Graphs - An Axiomatic Approach

Jadwiga Sosnowska, Oskar Skibski
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
Given this, we define a notion of the path evaluation function that assesses a path between two nodes by looking not only on the sum of edge weights, but also on the number of intermediaries.  ...  We study the problem of extending the classic centrality measures to weighted graphs.  ...  Acknowledgments Jadwiga Sosnowska and Oskar Skibski were supported by the Foundation for Polish Science within the Homing programme (Project title: "Centrality Measures: from Theory to Applications").  ... 
doi:10.24963/ijcai.2018/536 dblp:conf/ijcai/SosnowskaS18 fatcat:eq32bdqcjvfzbiyvyiutmqmnma

PageRank and The K-Means Clustering Algorithm [article]

Mustafa Hajij, Eyad Said, Robert Todd
2021 arXiv   pre-print
We demonstrate that PageRank and other centrality measures can be used in our setting to robustly compute centrality of nodes in a given graph.  ...  We utilize the PageRank vector to generalize the k-means clustering algorithm to directed and undirected graphs.  ...  PageRank and Other Centrality Measures The PageRank function [4] defined on the nodes of a graph can be viewed as centrality measure.  ... 
arXiv:2005.04774v3 fatcat:abbk5b3dyjffnomvgbzkyplyme

Generalized K-means for Metric Space Clustering Using PageRank

Mustafa Hajij, Eyad Said, Robert Todd
2020 Computer Graphics and Visual Computing  
We demonstrate that PageRank and other centrality measures can be used in our setting to robustly compute centrality of nodes in a given graph.  ...  We utilize the PageRank vector to generalize the k-means clustering algorithm to directed and undirected graphs.  ...  PageRank and Other Centrality Measures The PageRank function [BP98] defined on the nodes of a graph can be viewed as centrality measure.  ... 
doi:10.2312/cgvc.20201152 dblp:conf/tpcg/HajijST20 fatcat:u33c7gxuojcjrc3vbbyxvakbfe

Functional centrality in graphs

J. A. Rodríguez, E. Estrada, A. Gutiérrez
2007 Linear and multilinear algebra  
In this paper we introduce the functional centrality as a generalization of the subgraph centrality.  ...  We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node.  ...  Functional centrality The following well-known result will be useful in the spectral study of centralities. THEOREM 1 [2] Let v i and v j be vertices of a graph À.  ... 
doi:10.1080/03081080601002221 fatcat:osm3ebu6afgw7gl4glwqrq7mhe

Anisotropic Radial Layout for Visualizing Centrality and Structure in Graphs [article]

Mukund Raj, Ross T. Whitaker
2018 arXiv   pre-print
This paper presents a novel method for layout of undirected graphs, where nodes (vertices) are constrained to lie on a set of nested, simple, closed curves.  ...  The proposed approach modifies the multidimensional scaling (MDS) stress to include the estimation of a vertex depth or centrality field as well as a term that penalizes discord between structural centrality  ...  Graph centrality is a type of data depth on the nodes of a graph, and here we pursue layout methods that convey these depth properties. .  ... 
arXiv:1709.00804v2 fatcat:heb5inh3vfevbmyb3uvagor3cm

Anisotropic Radial Layout for Visualizing Centrality and Structure in Graphs [chapter]

Mukund Raj, Ross T. Whitaker
2018 Lecture Notes in Computer Science  
This paper presents a novel method for layout of undirected graphs, where nodes (vertices) are constrained to lie on a set of nested, simple, closed curves.  ...  The proposed approach modifies the multidimensional scaling (MDS) stress to include the estimation of a vertex depth or centrality field as well as a term that penalizes discord between structural centrality  ...  Graph centrality is a type of data depth on the nodes of a graph, and here we pursue layout methods that convey these depth properties. .  ... 
doi:10.1007/978-3-319-73915-1_28 fatcat:7wmsocgw5rem7nmj5oyxnzaofq

Testing centralization in random graphs

Christian Tallberg
2004 Social Networks  
In addition, critical values of the tests are modeled conditional on graph parameters via a linear regression model. An application is illustrated with analysis on a real data set.  ...  By carrying out a simulation study the performance of the tests is evaluated by comparing their power functions.  ...  Tests of centrality In this paper, we consider eight tests of graph centralization based on well-known graph centralization indices which share the property of measuring graph centralization as the variability  ... 
doi:10.1016/j.socnet.2004.02.001 fatcat:igb4odihtba3rc6ixkm7jt7m3y

Belief Functions for the Importance Assessment in Multiplex Networks [chapter]

Alexander Lepskiy, Natalia Meshcheryakova
2020 Communications in Computer and Information Science  
Additionally, we establish analytical relations between a proposed measure and classical centrality measures for particular graph configurations.  ...  We estimate cooperation of each node with different groups of vertices that surround it via construction of belief functions.  ...  The article was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE University) and supported within the framework of a subsidy  ... 
doi:10.1007/978-3-030-50143-3_22 fatcat:ndw2x7so4nejxj5yzarqyhpzcu
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