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Algorithms and Models for Network Data and Link Analysis 无水印pdf
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Algorithms and Models for Network Data and Link Analysis
Network data are produced automatically by everyday interactions – social networks, power
grids, and citations between documents are a few examples. Such data capture social and
economic behavior in a form that can be analyzed using powerful computational tools. This
book is a guide to both basic and advanced techniques and algorithms for extracting useful
information from network data. The content is organized around “tasks,” grouping the
algorithms needed to gather specific types of information and thus answer specific types of
questions. Examples include similarity between nodes in a network, prestige or centrality of
individual nodes, and dense regions or communities in a network. Algorithms are derived
in detail and summarized in pseudo-code. The book is intended primarily for computer
scientists, engineers, statisticians, and physicists, but is accessible to network scientists
based in the social sciences. Matlab/Octave code illustrating some of the algorithms will
gradually be available at:
http://www.cambridge.org/9781107125773.
Franc¸ois Fouss, Marco Saerens, and Masashi Shimbo received their Ph.D. degrees respec-
tively from the Universit
´
e catholique de Louvain, Belgium; the Universit
´
e Libre de Brux-
elles, Belgium; and Kyoto University, Japan. Franc¸ois Fouss and Marco Saerens are cur-
rently professors in computer science at the Universit
´
e catholique de Louvain, Belgium,
and Masashi Shimbo is associate professor at the Graduate School of Information Science,
Nara Institute of Science and Technology, Japan. Their research and teaching interests
include artificial intelligence, data mining, machine learning, pattern recognition, and nat-
ural language processing, with a focus on graph-based techniques.
23:20:58,
23:20:58,
Algorithms and Models for
Network Data and Link Analysis
Franc¸ois Fouss
Universit
´
e catholique de Louvain
Marco Saerens
Universit
´
e catholique de Louvain
Masashi Shimbo
Nara Institute of Science and Technology
23:20:58,
One Liberty Plaza, 20th Floor, New York, NY 10006, USA
Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminating knowledge in the pursuit of
education, learning, and research at the highest international levels of excellence.
www.cambridge.org
Information on this title: www.cambridge.org/9781107125773
©Franc¸ois Fouss, Marco Saerens, and Masashi Shimbo 2016
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2016
Printed in the United States of America by Sheridan Books, Inc.
A catalogue record for this publication is available from the British Library.
Library of Congress Cataloguing in Publication Data
Fouss, Franpcois, author. | Saerens, Marco, author. | Shimbo, Masashi, author.
Algorithms and models for network data and link analysis / Franpcois Fouss, Universitbe catholique
de Louvain, Marco Saerens, Universitbe catholique de Louvain, Masashi Shimbo, Nara Institute of
Science and Technology.
Cambridge, United Kingdom; New York: Cambridge University Press, 2016. | Includes
bibliographical references and index.
LCCN 2016008448 | ISBN 9781107125773 (hardback : alk. paper)
LCSH: Network analysis (Planning) – Mathematics.
LCC T57.85 .F68 2016 | DDC 004.6/5–dc23
LC record available at https://lccn.loc.gov/2016008448
ISBN 978-1-107-12577-3 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy of
URLs for external or third-party Internet Web sites referred to in this publication and
does not guarantee that any content on such Web sites is, or will remain, accurate or
appropriate.
23:20:58,
Contents
List of Algorithms page xiii
List of Symbols and Notation xvii
Preface xxiii
1 Preliminaries and Notation 1
1.1 Introduction 1
1.2 Content of the Book 3
1.3 Basic Definitions and Notation 6
1.3.1 Basic Graph Concepts
7
1.3.2 Standard Associated Matrices 11
1.3.3 Exploring the Graph and Cutting the Graph
into Smaller Pieces
20
1.4 Building a Graph from Data 22
1.4.1 -Neighbor Graph
23
1.4.2 k-Nearest Neighbor Graph 24
1.4.3 Mutual k-NN Graph 24
1.5 Basic Markov Chain Concepts 25
1.5.1 Transition Matrix
25
1.5.2 Multistep Transition Matrix 26
1.5.3 Some Properties of Markov Chains and States 27
1.5.4 Defining a Random Walk Model on a Graph 29
1.5.5 Stationary Distribution of a Regular Markov Chain 30
1.5.6 Stationary Distribution of a Random Walk on an
Undirected Graph
31
1.5.7 Fundamental Matrix of a Killed Random Walk 32
1.5.8 Stochastic Complementation 32
1.6 Average First Passage Time, Average Commute Time, and
Related Quantities 34
1.6.1 A Generic Quantity: Expected Cost before Absorption
34
1.6.2 Average First Passage Cost 36
1.6.3 Average First Passage Time and Average Commute Time 36
1.6.4 Probabilities of Absorption 37
1.6.5 Expected Number of Visits 38
1.7 Basic Notions about Kernels on a Graph 38
1.7.1 Kernel Matrix
39
1.7.2 Kernels on a Graph 41
1.7.3 Useful Transformations of the Kernel Matrix 41
v
23:20:44,
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