NDLI: Network science meets circuit theory: Kirchhoff index of a graph and the power of node-to-datum resistance matrix

Content Provider	IEEE Xplore Digital Library
Author	Yadav, M. Thulasiraman, K.
Copyright Year	2015
Description	Author affiliation: Sch. of Comput. Sci., Univ. of Oklahoma, Norman, OK, USA (Yadav, M.; Thulasiraman, K.)
Abstract	The emerging area of network science studies the properties of networks and dynamic processes on networks (such as spread of epidemics) that arises in a variety of applications including electrical, communication, internet, biological, ecological networks etc. Treating each element of a graph as a resistance, Kirchhoff index defined by the chemistry community is the sum of the effective resistances across all pairs of nodes of the graph. This index has been studied using the graph Laplacian (same as the indefinite admittance matrix). In this paper we present a simpler formula for Kirchhoff index based on the properties of the node-to-datum resistance matrix, considerably reducing the computational effort. A byproduct of this formula is a new invariant property of node-to-conductance matrix that does not depend on the choice of the datum node, extending the currently available knowledge on the determinant of the node-to-conductance matrix. Furthermore it can be shown that link congestion (if random-walk routing is used) can be estimated using the elements of the node-to-datum resistance matrix.
Starting Page	854
Ending Page	857
File Size	325946
Page Count	4
File Format	PDF
ISBN	9781479983919
DOI	10.1109/ISCAS.2015.7168768
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-05-24
Publisher Place	Portugal
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Laplace equations Indexes Resistance Immune system Routing Communities Admittance
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in