Naval Postgraduate School
Dudley Knox Library
NPS Dudley Knox Library
View Item 
  •   Calhoun Home
  • Faculty and Researchers
  • Faculty and Researchers' Publications
  • View Item
  •   Calhoun Home
  • Faculty and Researchers
  • Faculty and Researchers' Publications
  • View Item
  • How to search in Calhoun
  • My Accounts
  • Ask a Librarian
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

All of CalhounCollectionsThis Collection

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

The Neighbor Matrix: Generalizing A Graph’s Degree Sequence

Thumbnail
Download
Icon1510-06952.pdf (471.1Kb)
Download Record
Download to EndNote/RefMan (RIS)
Download to BibTex
Author
Roginski, Jonathan W.
Gera, Ralucca M.
Rye, Erik C.
Date
2016-08
Metadata
Show full item record
Abstract
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree sequence, a list of the adjacency matrix row sums. The distance matrix shows more information, namely the length of shortest paths between vertex pairs. We introduce and explore the neighborhood matrix, which we have found to be an analog to the distance matrix what the degree sequence is to the adjacency matrix. The neighbor matrix includes the degree sequence as its first column and the sequence of all other distances in the graph up to the graph’s diameter, enumerating the number of neighbors each vertex has at every distance present in the graph. We prove this matrix to contain eleven oft-used graph statistics and topological descriptors. We also provide insight into two applications that show potential utility of the neighbor matrix in comparing graphs and identifying topologically significant vertices in a graph.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
URI
https://hdl.handle.net/10945/65309
Collections
  • Faculty and Researchers' Publications

Related items

Showing items related by title, author, creator and subject.

  • Thumbnail

    The Neighbor Matrix: generalizing the degree sequence 

    Roginski, Jonathan W.; Gera, Ralucca M.; Rye, Eric C. (American Mathematical Society, 2015-10-19);
    The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized ...
  • Thumbnail

    THE DISTANCE CENTRALITY: MEASURING STRUCTURAL DISRUPTION OF A NETWORK 

    Roginski, Jonathan W. (Monterey, CA; Naval Postgraduate School, 2018-06);
    This research provides an innovative approach to identifying the influence of vertices on the topology of a graph by introducing and exploring the neighbor matrix and distance centrality. The neighbor matrix depicts the ...
  • Thumbnail

    Network monitoring method using phantom nodes 

    Johnson, Jamie Lynn; Parker, Thomas; Tummala, Murali; McEachen, John C. (The United States of America as represented by the Secretary of the Navy, Washington, DC (US), 2018-05-01);
    Determining flow rules in a software defined network (SDN) of a plurality of forwarding devices includes determining, by a controller device, a network adjacency matrix of the SDN, wherein the network adjacency matrix ...
NPS Dudley Knox LibraryDUDLEY KNOX LIBRARY
Feedback

411 Dyer Rd. Bldg. 339
Monterey, CA 93943
circdesk@nps.edu
(831) 656-2947
DSN 756-2947

    Federal Depository Library      


Start Your Research

Research Guides
Academic Writing
Ask a Librarian
Copyright at NPS
Graduate Writing Center
How to Cite
Library Liaisons
Research Tools
Thesis Processing Office

Find & Download

Databases List
Articles, Books & More
NPS Theses
NPS Faculty Publications: Calhoun
Journal Titles
Course Reserves

Use the Library

My Accounts
Request Article or Book
Borrow, Renew, Return
Tech Help
Remote Access
Workshops & Tours

For Faculty & Researchers
For International Students
For Alumni

Print, Copy, Scan, Fax
Rooms & Study Spaces
Floor Map
Computers & Software
Adapters, Lockers & More

Collections

NPS Archive: Calhoun
Restricted Resources
Special Collections & Archives
Federal Depository
Homeland Security Digital Library

About

Hours
Library Staff
About Us
Special Exhibits
Policies
Our Affiliates
Visit Us

NPS-Licensed Resources—Terms & Conditions
Copyright Notice

Naval Postgraduate School

Naval Postgraduate School
1 University Circle, Monterey, CA 93943
Driving Directions | Campus Map

This is an official U.S. Navy Website |  Please read our Privacy Policy Notice  |  FOIA |  Section 508 |  No FEAR Act |  Whistleblower Protection |  Copyright and Accessibility |  Contact Webmaster

Export search results

The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

A logged-in user can export up to 15000 items. If you're not logged in, you can export no more than 500 items.

To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.