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99 Nw. U. L. Rev. 1687 (2004-2005)
On the Regulation of Networks as Complex Systems: A Graph Theory Approach

handle is hein.journals/illlr99 and id is 1697 raw text is: Copyright 2005 by Northwestern University, School of Law                    Printed in U.S.A.
Northwestern University Law Review                                           Vol. 99, No. 4
Essay
ON THE REGULATION OF NETWORKS AS
COMPLEX SYSTEMS: A GRAPH THEORY
APPROACH
Daniel F. Spulber'& Christopher S. Yoo*
I.   IN TRODUCTION   ...................................................................................................  1687
II.  NETWORKS AS COMPLEX    SYSTEMS ..................................................................... 1693
III. GRAPH THEORY AND NETWORK CONFIGURATION ............................................... 1695
A.   Cost Minimization as a Determinant of Network Configuration ............... 1695
B.   Reliability as a Determinant of Network Configuration ............................ 1699
C. Interactions Between Cost and Capacity. Economies of Scale ................ 1701
IV. GRAPH THEORY AND NETWORK CAPACITY ........................................................ 1703
A.   The M ax-Flow/M in-Cut Theorem  ............................................................. 1703
B.   Implications of the Max-Flow/Min-Cut Theorem for Network Policy ....... 1705
V. THE POLICY IMPLICATIONS OF A GRAPH THEORETICAL APPROACH ..................... 1707
A.   The Impact of Interconnection and UNE Access ....................................... 1707
B.   The Shortcomings of the Cost-Based Pricing ............................................ 1709
C. Limitations on Basing Prices on Market Benchmarks .............................. 1713
D.   CompelledAccess to Broadband Networks ............................................... 1716
E.   The Regulation of Voice over Internet Protocol (VoIP) ........................ 1718
F.   A Formal Methodology for Calculating Regulatory Rates ........................ 1719
V I.  C ON CLU SION   ......................................................................................................  172 1
I. INTRODUCTION
One of the most salient economic developments of the last decade has
been the transformation of the telecommunications industry. Competition
Elinor Hobbs Distinguished Professor of International Business, Kellogg School of Management,
and Professor of Law, Northwestern University School of Law.
Professor of Law, Vanderbilt University Law School. We would like to thank Paul Edelman,
Chris Guthrie, Todd Henderson, Lou Kaplow, Vik Khanna, Jeff MacKie-Mason, Richard Nagareda,
Randy Picker, Bob Rasmussen, Sang-Seung Yi, Kiho Yoon and participants in a workshop conducted at
the 15th Annual Meeting of the American Law and Economics Association, the University of Michigan
Law School Workshop on Cyberlaw and Economics, and the Seoul National University Center for Law
and Technology for comments on earlier drafts of this Essay. We plan to offer a more extended and
formal treatment of this subject in a book entitled Networks in Telecommunications: Economics and
Law, which is forthcoming on Cambridge University Press.

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