Connections
Volume 35 Issue 2
February 2016
Official Journal of the International Network for Social Network Analysis
Connections publishes original empirical articles that
apply social network analysis. We are particularly interested in research
reports, articles demonstrating methodological innovations and novel
research design. We also facilitate the dissemination of datasets and
review scholarly books. Our scope spans many disciplines and domains
including Communication, Anthropology, Sociology, Psychology,
Organizational Behavior, Knowledge Management, Marketing,
Social Psychology, Political Science, Public Health, Policy Studies,
Medicine, Physics, Economics, Mathematics, and Computer Science.
As the official journal for the International Network for Social Network
Analysis (INSNA), the emphasis of the publication is to reflect the
ever-growing and continually expanding community of scholars using
network analytic techniques.
Cover image: Doreian, this issue pg. 14
Former Connections Editors
Barry Wellman
Founding Editor
1976-1988
Susan Greenbaum
1987-1990
Alvin Wolfe
1990-1993
John Skvoretz
1993-1997
Katherine Faust
1993-1997
Steve Borgatti
1997-2000
Bill Richards
2000-2003
Tom Valente
2003-2011
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Manuscripts are selected for publication after a double-blind peer review process. Instructions for manuscript
submissions on the back cover of this journal and for subscription information email the Editorial Manager at
amoritia@insna.org. We are dedicated to academic open access, all articles published in Connections are available
free of charge through our website www.insna.org
Dimitris Christopoulos, Editor
MODUL University, Vienna, Austria
Amoritia Strogen-Hewett, Editorial & Copyediting Management
JulNet Solutions, Huntington, WV, USA
Editorial Headquarters
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Department of Public Governance & Sustainable Development
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Editorial Board
Bruce Cronin
University of Greenwich
Ian McCulloh
John Hopkins University
Jana Diesner
University of Illinois at UC
Susie J. Pak
St. John’s University
Dan Halgin
University of Kentucky
Juergen Pfeffer
Carnegie Mellon University
Kayla de la Haye
University of Southern California
Meredith Rolfe
London School of Economics
Nicholas Harrigan
Singapore Management University
Kerstin Sailer
University College London
Betina Hollstein
University of Bremen
David Shaefer
Arizona State University
Karin Ingold
University of Bern
Christophe Sohn
LISER-Luxembourg
Rich de Jordy
Northeastern University
Olivier Walther
University of Southern Denmark
DEN Section Editor
Juegen Pfeffer
Carnegie Mellon University
From the Editor
I am proud to introduce a new issue of Connections. In this issue you can find articles on: structural
balance in signed networks (Doreian and Mrvar); operationalising oligarchic networks as rich clubs
(Ansell, Bichir, Zhou); the use of experiments in social exchange networks (Neuhofer, Reindl and
Kittel); Tom Valente’s keynote on network influences on behaviour (Dyal); description of a dataset from
a network exchange experiment (Skvoretz); and the description of a dataset from a health promotion
study (Gesell and Tesdahl).
In the last few years we have introduced a section on datasets, codebooks and data collection methods
(DEN); state of the art reviews; and the professionalization of the production process with the assignment
of DOI numbers and copyright agreements with authors. Beyond our regular call for original research
articles, I would like to invite submissions on network research design as a new section to the journal.
Of particular interest are studies where the use of novel research designs reflect on the choice between
alternative models.
The journal is moving towards distributed editorship, emulating the model adopted by Network Science
as most pertinent for an interdisciplinary audience. We will shortly circulate the list of area specific
editors.
We are looking forward to your suggestions and feedback at Sunbelt and via email. We are organising a
short reception on Wednesday the 6th of April at 8pm at the Presidential Suite of the Marriot Hotel (i.e.
the Hospitality Suite) and we would like to invite all authors, potential authors and friends of the journal
to come and meet the Editorial Board.
Dimitris Christopoulos
Editor, Connections
www.dimitriscc.wordpress.com
Table of Contents
Research Articles
Identifying Fragments in Networks for Structural Balance and Tracking the Levels of Balance
Over Time
Patrick Doreian & Andrej Mrvar
6
Who Says Networks, Says Oligarchy? Oligarchies as “Rich Club” Networks
Christopher Ansell, Renata Bichir & Shi Zhou
20
Social Exchange Networks: A Review of Experimental Studies
Sabine Neuhofer, Ilona Reindl & Bernhard Kittel
34
Network Influences on Behavior: A Summary of Tom Valente’s Keynote Address at Sunbelt
XXXV: The Annual Meeting of the International Network for Social Network Analysis
Stephanie Dyal
52
Data Exchange Network
The South Carolina Network Exchange Datasets
John Skvoretz
58
The “Madre Sana” Dataset
Sabina Gesell & Eric Tesdahl
62
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Who Says Networks, Says Oligarchy? Oligarchies as “Rich Club” Networks
Christopher Ansell
University of California
Berkeley, CA, USA
Renata Bichir
University of São Paulo
São Paulo, Brazil
Shi Zhou
University College London
London (UCL), UK
Abstract
Departing from Roberto Michels’s classic analysis of oligarchy, we provide a structural analysis of the concept based
on social network analysis. We define oligarchy as a social network that exhibits three structural properties: tight
interconnections among a small group of prominent actors who form an “inner circle”; the organization of other actors
in the network through the intermediation of this inner circle; and weak direct connections among the actors outside
the inner circle. We treat oligarchy as a global property of social networks and offer an approach for measuring the
oligarchical tendencies of any social network. Our main contribution is to operationalize this idea using a “rich club”
approach. We demonstrate the efficacy of this approach by analyzing and comparing several urban networks: Sao
Paulo urban infrastructure networks and Los Angeles and Chicago transportation policy networks.
Keywords: oligarchy, rich clubs, policy networks, urban networks
Authors
Christopher Ansell, Department of Political Science, University of California, Berkeley, California, USA.
Renata Bichir, Center for Metropolitan Studies, Center of Arts, Sciences and Humanities, University of São Paulo,
São Paulo, Brazil.
Shi Zhou, Department of Computer Science, University of College London (UCL), London, UK.
Acknowledgements
We would like to thank Margaret Weir and Eduardo Marques for allowing us to use relational data they collected on,
respectively, Chicago and Los Angeles transportation networks and Sao Paulo urban infrastructure networks.
Correspondence concerning this work should be addressed to Christopher Ansell by email: cansell@berkeley.edu
20 | Volume 35 | Issue 2 | insna.org
DOI: http://dx.doi.org/10.17266/35.2.2
Oligarchies as “Rich Club” Networks
1. Introduction
The concept of oligarchy has a long history in the
social sciences and in the popular imagination, from
Aristotle’s description of oligarchy as rule by the few,
to Roberto Michel’s “Iron Law of Oligarchy,” to the
colloquial description of post-Soviet capitalist grandees
as “oligarchs.” The term has various connotations in the
social sciences, from the “bureaucratic conservatism”
of social movements (Voss and Sherman 2000), to the
control of the economy by “industrial tycoons” (Guriev
and Rachinsky 2005), to the domination of politics by
“major producers” (Acemoglu 2008). Most of these
references, however, share the idea that an oligarchy is
a regime controlled by cooperation or collusion among a
small group of powerful elites.
Given the long history and ubiquitous use of
the idea of oligarchy and the potential importance of
oligarchical control over social movements, economies,
and political systems, it is surprising that there is so little
theoretical and empirical attention paid to the concept
of oligarchy. Many authors make reference, of course,
to Roberto Michels’s work, Political Parties, which
provides the classic theoretical treatment of the concept.
But since the publication of this important work in 1910,
there has been limited theoretical analysis of the concept
of oligarchy. Taking Michels’s claim that oligarchies
were inevitable seriously, subsequent scholarship has
mostly sought to identify the conditions under which
organizations and social movements do not become
oligarchical (Lipset, Trow, and Coleman 1977; Voss and
Sherman 2000). In this paper we build on, but go beyond
Michels’s classic treatment by analyzing the structural
bases of oligarchy, which we operationalize using social
network analysis. We treat oligarchy as a global property
of social networks and offer an approach for measuring
the oligarchical tendencies of any social network.
We begin by briefly reviewing Roberto Michels’s
classic analysis of oligarchy, pointing to how it provides
the basis for our own structural analysis. A protégé of Max
Weber’s, Michels analyzed the development of oligarchy
in complex bureaucratic organizations. His central
insight was a synthesis of the “elite theory” of fellow
Italians Gaetano Mosca and Vilfredo Pareto with Weber’s
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expectation that modern bureaucracy could become an
“iron cage.” He argued that organizational differentiation
and stratification produced a distinctive, self-perpetuating
elite (“Who says organization, says oligarchy”). Though
formally sovereign, the “masses” were unable to organize
themselves and as a result become dependent on the elite
group to direct them. While the elite group is composed
of a stable “inner circle” that monopolizes control
over organizational offices, the average member has a
narrow and unstable relationship with the organization.
Consequently, the elite’s advantages allow them to
transform their “inner circle” into a “closed caste.” This
closure is essential if elites are to prevent a challenge to
their position by the rank-and-file. In sum, an oligarchy
has three aspects: the elite are tightly interconnected
among themselves, forming an “inner circle”; the masses
are organized through the intermediation of this inner
circle; and the masses are poorly interconnected among
themselves.
Literature in the Michelsian tradition has focused
on the organizational aspects of oligarchy.1 By contrast,
we focus on the relational character of oligarchy, as it
might develop within a social network. A social network
perspective has two important advantages for the study of
oligarchy. First, it frees us from the confines of a single
organization and allows us to examine how relationships
might structure the organization of elites spanning
organizational or institutional boundaries (see Marques
(2000, 2003, 2008, and 2012) on the permeability of the
“State fabric”2). Second, a social network perspective
may be used to capture the informal relational basis of
oligarchy—the proverbial ‘old boys network.’
An earlier generation of scholars made much
the same argument and closely dissected the structure of
relationships among “ruling elites” (Hunter 1953, Mills
1956, Dumhoff 1967). But this scholarship got bogged
down in debates between “elite theorists” and “pluralists”
(Polsby 1960, Dahl 1961). Although this debate generated
new insights, it tended to be structured in dichotomous
terms as an issue of whether or not a ruling elite existed.
In the 1970s, work in this tradition shifted its attention
to one specific type of network—“interlocks” between
the boards of corporations. As this corporate interlock
literature developed, it increasingly focused on how links
1 See Leach (2005) for a review and critique. He defines oligarchy as the “concentration of entrenched illegitimate authority and/or influence
in the hands of a minority...” (2005, 329).
2 This concept refers to the relational patterns formed by both institutional and personal relationships that structure state organizations.
According to Marques: “The state fabric is created and changed by networks among people and organizations, both inside the state and in the
larger environment of policy communities. The contacts are both personal and institutional and are based in old and new ties, constantly recreated. These midlevel structures control several resources and affect preferences, restrict choices and strategies, and change political results”
(2012, 33).
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between corporate boards shaped the flow of influence
and resources between them (Mizruchi 1996). These
studies usefully widened the discussion of the role of
corporate interlocks, but also gradually shifted attention
away from the regime-like characteristics of interlocking
directorates.
We have no interest in resurrecting the old elitepluralist debate. Our relational approach to oligarchy
suggests that the structure of social networks is likely
to affect the flow of information, the distribution of
resources, patterns of decision-making and influence.
But to be clear, a structural analysis of networks alone
does not provide sufficient behavioral evidence that a
ruling elite monopolizes power and influence; it can only
demonstrate that the relational basis for such control or
influence exists. In addition, as our analysis will show,
we depart from the more dichotomous inclinations of the
elite-pluralist debate, focusing instead on how to measure
oligarchical tendencies in networks.
Why is a relational concept of oligarchy useful?
One way to approach this question is through the idea of
brokerage. Brokerage is a form of intermediation where a
focal actor, the broker, mediates the relationship between
some other set of actors. Social network analysis has a
well-established tradition examining this brokerage role
(Simmel 1950; Gould and Fernandez 1989; Burt 2005;
Obstfeld 2005; Stovel and Staw 2012). The focus of this
tradition has been to understand the position and power of
individual brokers, and the advantages that accrue to them
or those they connect. However, in many cases, it is also
interesting or valuable to understand the collective pattern
of mediation in a network. The concept of oligarchy, we
suggest, points to the collective mediation of a network
by a small but cohesive subgroup. To explain this point,
recall the three aspects of oligarchy that we drew from
Michels: the elite are tightly interconnected among
themselves, forming an “inner circle”; the “masses”
are organized through the intermediation of this inner
circle; and the masses are poorly interconnected among
themselves. An oligarchy describes a network where a
cohesive subgroup monopolizes the intermediation of
relationships in the network as a whole. As in the work on
individual brokerage, Michels suggests that advantages
accrue to the inner circle. But the concept of oligarchy is
about the collective, rather than individual intermediation
of the network.
Pure oligarchies may rarely exist. Nevertheless,
many kinds of social networks may have oligarchical
tendencies. It is well established in the social network
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Oligarchies as “Rich Club” Networks
literature that some nodes are often much more central
than others and that these central nodes may play an
important brokerage role, often by spanning “structural
holes” in the network. We also know that subgroups form
within networks, often among well-connected actors, and
that networks often exhibit center-periphery patterns.
Work on “small world” networks has also found that
a small group of “hubs” can link a sparsely connected
network together (Watts 1999). When taken together,
these findings suggest the possibility for cohesive
subgroups to dominate or monopolize the intermediation
of the network as a whole. It is more useful, however,
to understand the degree to which a social network is
collectively intermediated than to become fixated on
whether or not a network has a ruling elite.
In the following section, we develop a strategy for
measuring the oligarchical tendencies of a network using
a “distribution of degree” approach. In later sections of
the paper, we demonstrate the value of this approach by
analyzing several social networks.
2. Three Network Metrics
How should we identify the tendency of a social
network to be oligarchical? The tool kit of social network
analysis offers several possibilities. In this paper, we
introduce a method based on work in physics and
computer science that focuses on how ties are distributed
across the network. We use the concept of “rich clubs”
(Zhou and Mondragón 2004; Zhou and Mondragón 2007,
Mondragón and Zhou 2009) as our basic measure of the
oligarchical tendencies of a network, and supplement
it with an analysis of the “mixing properties” of
networks (Newman 2002) and the degree distribution
of ties (Barabasi and Albert 1999). Taken together,
these measures identify the tendency of social networks
to exhibit the key features of oligarchy that we have
identified: the existence of a small, cohesive group that
monopolizes the intermediation of the rest of the network.
2.1 Power-Law Degree Distribution
Many real networks – especially large and complex ones
– may display a skewed degree distribution known as the
“power law,” or P(k) ~ k -Y , where degree k is defined
as the number of links a node has (Barabási and Albert,
1999; Xu, Zhang and Small, 2010). A power-law network
is called ‘scale-free’ because it is not the average degree,
but the exponent of the power-law distribution, that
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Oligarchies as “Rich Club” Networks
characterizes the network’s connectivity.3
In a power-law network, most nodes have only a
few links, and the network is guaranteed to have a small
set of nodes with very high degrees, order(s) of magnitude
higher than the average degree expected from a random
process. Thus, for power-law networks, it is particularly
important to examine the role of the high-degree nodes in
organizing the network’s global structure.
2.2 Network Mixing Patterns
Newman (2002) identified different mixing patterns in
networks. A network is assortative if nodes of similar
degrees tend to be connected to one another and
disassortative if nodes tend to be connected to nodes
of different degrees. To measure these different mixing
patterns, Newman proposed the assortative coefficient r,
which ranges from -1 to 1. When r = 1, there is perfect
assortative mixing in the network, i.e., every link connects
two nodes with the same degree; when r = -1, there is a
perfect disassortative network, i.e., every link connects
two nodes with different degrees; when r = 0, there is a
neutral mixing network.
2.3 Rich-Club Coefficient
The “rich club” concept proposed by Zhou and Mondragon
(2004, 2007 and 2009) complements this discussion of
network mixing patterns. In doing so, it addresses the
following ambiguities. For example, if a network displays
assortative mixing where high-degree nodes tend to link
with other high-degree nodes, does this mean the highdegree nodes are tightly (or fully) interconnected with
each other? Or, if a network is disassortative and highdegree nodes (on average) tend to link with low-degree
nodes, does this mean the high-degree nodes do not link
with themselves at all?
“Rich” nodes are defined as a group of nodes
with the highest degrees in a network, specified either
as the top n best-connected nodes or as the nodes with
degrees larger than or equal to a given degree k. For a
given group of rich nodes, any member of the group has
a degree higher than or equal to any node outside the
group. More nodes with lower degrees are included when
the size of the group increases.
The rich-club coefficient Ø is defined as the ratio
of the actual number of links to the maximum possible
number of links among a group of rich nodes (Zhou and
Mondragon 2004, 2007).4 It is a quantitative measure of
the density of connectivity among a given group of rich
nodes. When Ø=1, the rich nodes are fully interconnected,
forming a clique. When Ø=0, the rich nodes have no direct
link among themselves (although each of them may have
a large number of links with nodes outside the group).
For simplicity, a network is said to contain a rich
club if the richest nodes (e.g. the top 5% best-connected
nodes) have a high value rich-club coefficient (say, Ø
> 0.5). No a priori definition exists to determine which
nodes are in the rich club. The rich-club coefficient is
usually calculated for all groups of rich nodes so that this
structural property can be examined across all levels of
network hierarchy.5 The rich-club coefficient has been
found to be critically relevant to the redundancy and
robustness of a network (Zhou and Mondragón 2004b)
and to its routing efficiency in terms of shortest paths
between nodes (Zhou 2009).
Zhou and Mondragon (2007) shows that a
network’s rich-club coefficient is not trivially related
with the network’s degree distribution or mixing
pattern. For example, networks having exactly the same
degree distribution can have a vastly different rich-club
coefficient; and high-degree nodes in an assortative
network are not necessarily more interconnected than
those in a disassortative network.
2.4 Debate on the Rich-Club Phenomenon
There has been a debate on the rich-club phenomenon with
respect to how to determine whether the rich nodes in a
network show a tendency to form a tightly interconnected
club. Colizza et al. (2006) propose to compare the richclub coefficient of a real network against a null model
defined as the average of a maximally randomized
version of the real network. The logic here is analogous
to the difficulty of determining whether a person is “tall”
or “short” without comparing their height to the average
height of the group of people that the person belongs to.
One “surprising” result is that the Internet (AS graph),
which is considered to exemplify a strong rich-club
phenomenon, would have a slightly lower rich-club
3 This property derives from two main mechanisms of the power-law networks identified by Barabási and Albert (1999, p.509): (i) networks
expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. In other
words, the authors showed that large networks self-organize into a scale-free state, a feature unpredicted by previous random network models.
4 The maximum possible number of links among n nodes is n(n-1)/2.
5 When the group of rich nodes is given by the node rank n, the most exclusive group contains only the top 2 best-connected nodes (n=2), and
the largest group is the whole network (n=N). When the group is given by degree k, the smallest group has nodes with k=kmax where kmax is
the largest degree in the network, and the largest group contains all nodes with k >= 1.
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coefficient when the network is randomly rewired (while
preserving the original degree distribution). However,
this method cannot be used to compare between different
real networks – because a “short” person on a basketball
team may be taller than a “tall” person in a primary school
class.
Amaral and Guimera (2006) relate the rich-club
phenomenon to a monotonic increase of the rich-club
coefficient as a function of degree. They conjecture that
the monotonic increase may be “a natural consequence of
a stochastic process” and comment that “… an oligarchy
will always appear to be present, even if the network
is random.” However, it is widely known that the richclub coefficient is not a monotonic function in most real
networks (McAuley et al 2007; Opsahl et al 2008). The
rich-club coefficient can even be a bell-shaped function
in some networks (Zhou and Mondragon 2007).
Mondragon and Zhou (2007) argue that the richclub coefficient is an absolute measure of the density
of interconnectivity among a group of rich nodes. It is
calculated without any assumption and judgment about
the rich-club phenomenon. In other words, it is measuring
a person’s height without judging whether a person is
tall or not. In this paper we use the rich-club coefficient
as a network metric and avoid referring to the rich-club
phenomenon.
3. Oligarchy as a Global Property of Networks
Assortative mixing is common in social networks, but is
not associated with “oligarchical” networks. An oligarchy
is a rich club with disassortative mixing. In other words,
the “rich” nodes are interconnected, but they are also
connected to the “poor” nodes who are not strongly
interconnected among themselves.
The idea that the power of well-connected
people is derived from their connections to other wellconnected people is well established in social network
analysis, and typically measured using eigenvector
centrality (Bonacich 1972) or, in a form that allows you
to vary the relative importance of indirect ties, “power
centrality” (Bonacich 1987). One difficulty with the
later measure, however, is that it requires an arbitrary
decision on the part of the analyst about whether people
gain more power by being tied to other “rich” nodes or by
being tied to more “impoverished” nodes. Following this
tradition of measuring centrality and power in networks,
some authors have recently developed new measures
for identifying “leadership insularity” (Abersman
Oligarchies as “Rich Club” Networks
& Christakis, 2010) or “organizational influentials”
(Cole and Weiss, 2009).6 Similarly, classic strategies of
detecting cohesive subgroups (Wasserman and Faust
1994), such as clique analysis and its variants, or newer
methods of “community detection,” such as the GirvanNewman method (Newman 2004) may be quite useful for
identifying the “inner circles” of oligarchies.
The rich-club approach has a different focus
and purpose than these techniques. First, it expands
the analytical focus beyond identifying well-connected
leaders or important subgroups. “Rich” nodes form
a cohesive group among themselves, but they also
maintain ties to more “impoverished” nodes—e.g., their
clients. It is these ties with non-rich nodes that makes
rich nodes “rich.” Second, the rich-club approach aims to
characterize the oligarchical tendency of entire networks
as opposed to identifying the oligarchs themselves.
The rich-club approach uses the “mixing
properties” of the network to evaluate whether rich
nodes merely affiliate among themselves, or whether
they also affiliate with non-rich nodes. If a network is
“assortative,” rich nodes affiliate primarily with other
rich nodes, while non-rich nodes affiliate primarily with
other non-rich nodes (in an assortative network, nodes of
similar degree associate with each other). If a network is
“dissassortative,” by contrast, nodes of dissimilar degree
associate together. While the “rich club” measure captures
the way a core group monopolizes ties, the disassortative
measure guarantees that this core is not segmented off
from the rest of the network.
In addition to knowing that there is a group of
rich nodes who are tied together, but also linked to a
wider network of clients, the concept of oligarchy also
presumes that the “rich club” at the core of the network
is small relative to the network as a whole. One way to
evaluate whether the “rich club” is small is to examine
the degree distribution of the network. If the rich-club
is small, we should expect the degree distribution to
resemble a power law.
To summarize, an oligarchical network can be
characterized as having a “rich club” (a group of wellconnected nodes who are connected to one another),
but the overall network exhibits mixing properties that
are disassortative (where each rich node is strongly
connected to the poor nodes) and a power-law degree
distribution (few well-connected nodes and many poorlyconnected nodes). Taken together, these three properties
capture the degree to which a small group dominates the
collective intermediation of the network as a whole. In
6 Looking for the most influential individuals in school networks, Cole and Weiss (2009, 4) propose four methods: 1) absolute cut score (indegree score); 2) fixed percentage of population is defined as influential; 3) degree standard deviation; 4) random permutation.
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Oligarchies as “Rich Club” Networks
Michels’ terms, the rich club is a cohesive “inner circle”
that organizes the weakly organized “masses.”
One alternative way to identify an oligarchical
network regime is to develop a core-periphery analysis.
Much like the concept of an oligarchy, a core-periphery
structure is a “core” of people who are tied together and
a “periphery” of less well connected actors (Laumann
and Pappi 1976). Breiger describes a core-periphery
network as follows: “a coherent set of active members (or
a “leading crowd”) is surrounded by isolated individuals
who have interchange both to and from them” (1979,
29). Consistent with this definition, Borgatti and Everett
(1999) developed a partitioning algorithm for analyzing
core-periphery structure that assigns those who are
closely connected to each other (1-block) to the “core”
and those who are not connected to each other (0-block)
to a “periphery.” They then develop a “fitness measure” to
evaluate how closely the derived assignment corresponds
with an idealized core-periphery structure. However,
there are several limitations of using a core-periphery
analysis as measure of oligarchy:
1. The core-periphery algorithm partitions a
network into a core that is tightly interconnected
(1-block), but this measure does not directly
capture the degree to which this core is a “richclub” (as measured by the rich-club coefficient);
2. The core-periphery measure says that the core
is tightly interconnected and the periphery is
weakly interconnected; it says less about the link
between core and periphery (only that it expects
an imperfect 1-block). The rich club approach
directly measures how rich nodes are tied to
non-rich nodes (assortative and disassortative
mixing).
3. The “core” of a core-periphery structure might
be very large, while we are assuming that the
“rich club” is a small group (as measured by the
power law distribution).
measure of oligarchy. In the next section, we will analyze
several social networks using this rich-club approach:
urban infrastructure policy networks in São Paulo, Brazil
over six mayoral administrations and transportation
policy networks in two U.S. cities, Chicago and Los
Angeles. These networks allow us to compare urban
policy regimes across time in the same city (São Paulo)
and across city for the same kind of policy domain
(Chicago and Los Angeles), and across urban regimes in
two countries (Brazil and the U.S.).
4. Description of the Networks
4.1 São Paulo Urban Infrastructure Networks
São Paulo is the largest and most important metropolis
in Brazil and South America, with roughly 11.9 million
municipal inhabitants and 20 million in the metropolitan
region. Besides shaping the urban space in São Paulo,
urban-infrastructure policy is at the core of municipal
politics and policies, and receives a large share of the
municipal budget – 13% on average during the period
1975-2000 (Bichir, 2005). Thus, it is an influential and
important policy domain.
Policy network data was collected by Eduardo
Marques and Renata Bichir in order to investigate the
policy dynamics of the Secretariat of Public Roads
(“Secretaria de Vias Públicas” – SVP), the São Paulo
municipal agency responsible for urban infrastructure
policy (Marques, 2003).7 Based on an examination
of contract notices published in the official press, this
research analyzed spatial, relational, and political
dynamics of urban-infrastructure policy in the city of São
Paulo from 1975 to 2000.8
Thus, while core-periphery measures may also provide an
approximate measure of oligarchical structure, the richclub approach offers a more direct and discriminating
7 Urban infrastructure policy is a part of a broader “urban engineering” community that encompasses several policy domains, including
infrastructure, maintenance of the built environment and services, urban transportation, and cleaning (Marques, 2003). The municipal agency
responsible for urban infrastructure policy depends on the municipal budget, does not have strong institutional boundaries or civil service career
patterns, and experiences strong migrations from and to other parts of the government and the private sector (Marques, 2003). These institutional
features affect the policy network and the way policy is formulated and implemented.
8 In Brazil, all government contracts have to be published in official daily publications called “Diários Oficiais.” To obtain information on the
patterns of investment in urban infrastructure, the data set includes information on almost 5500 urban public works project contracts (road and
drainage work, river canalization, bridges and tunnel construction etc.) from 1975 to 2000.
insna.org | Issue 2| Volume 35 | 25
Connections
To recreate the policy network from 1975 to 2000, the
researchers conducted 26 in-depth interviews with career
officials, technicians, and members of the community of
engineers associated with SVP. These interviews sought
to characterize the policy and political dynamics in the
city over time, as well as to investigate the continuity
of the networks.9 The interviews used a name generator
– based on official data of all incumbents of the main
institutional positions of the Secretariat over time – and
snowballing techniques, to identify the complete network.
The network data analyzed in this paper is the data set
produced by the Marques team using this data collection
process.
This policy network was constructed with the aim
of analyzing the power dynamics inside this bureaucracy
under different mayors with different political inclinations.
The study focused on the differences between right-wing
and left wing parties, since this is a policy area traditionally
associated with the right in the city of São Paulo.10 The
relations among different groups of the Secretariat, the
broader political environment (political parties, other
public agencies), and private companies responsible for
public works were investigated. The analysis found that
this policy community is characterized by the importance
of personal ties among state actors and between state
and private sector actors (Marques, 2003, 2012). The
infrastructure policy network in São Paulo became more
dense and complex over time, from approximately 75
interconnected people prior to 1975 to more than 250
people in the administration of Celso Pitta (1997-2000).
Marques (2003) found a hegemonic group in control of
policy across this period, which was stable even during
the two left-wing administrations (Covas and Erundina)
despite their attempts to change the power dynamics in
this policy domain by introducing new players into the
policy network. These new actors, however, failed to
displace or break the hold of the hegemonic group.
Oligarchies as “Rich Club” Networks
Chicago and Los Angeles Transportation Policy Networks
Weir et al. (2009) collected data on the transportation
policy networks of the second and third largest U.S.
metropolitan regions — Los Angeles (13 million people)
and Chicago (9 million people). The purpose of the study
was to investigate whether the 1991 Intermodal Surface
Transportation Efficiency Act (ISTEA) had created
conditions for collaboration on transportation policy
issues among groups operating on an urban and regional
scale. ISTEA also sought to encourage the participation
of new groups typically excluded from previous planning
regimes. In addition to their size, L.A. and Chicago were
selected because they represent contrasting urban political
dynamics. L.A. is traditionally regarded as having a very
fragmented urban and regional politics, while Chicago’s
active business and civic community and centralized
political regime make it an example of more organized
and cohesive policy-making.
Semi-structured interviews were conducted
in 2003 with 41 groups active in transportation issues
in the Los Angeles region and in 2005 with 35 groups
active in the Chicago region. During these interviews,
groups were shown a list of organizations involved in
transportation issues and asked to “check every name on
the list that your organization has worked with as part
of its transportation work.” A follow-up question then
asked respondents to indicate which of these groups they
had worked with “closely.” The questions were intended
to capture the difference between “weak” and “strong”
network ties.
The study found that ISTEA had encouraged the
creation of new groups and that these groups brought
new perspectives to the urban and regional transportation
policy process. It was also found that these groups were
engaged in active networking within their regions. The
interviews, however, also indicated that the groups
9 Since this is a relatively stable and close community-many of the technicians studied together in the same universities, have common business
associations outside the public sector and are co-members of professional associations-the research team assumed that most people would
know each other, forming a one-mode network. Information on all types of contacts inside the policy community was considered, and not only
information on ties associated with some specific policy issues or contracts. In this sense, the relationship between two nodes may represent
several types of ties, including work ties, friendship ties, business ties, etc. The researchers did not exclude people from the network due to
retirement, only when someone died or went to a completely different sector. The interviews revealed that the retired public servants usually
went to the private sector and stayed as formal and informal consultants for the public sector. Additional interviews were then conducted in
order to separate contacts into different periods and to differentiate the types and strength of ties (indicated by the frequency of citation of each
dyad). These interviews allowed the construction of the network of relationships between individuals, entities and private companies in each
mayoral administration from 1975 to 2000.
10 The study characterized “right-wing” politicians as belonging to the party that supported the military regime (Arena) and the parties that
were created after it (PPB and PDS), including a party aligned with them at the municipal level (PTB). Thus, Olavo Setúbal (in charge of the
municipality from 16/04/1975 to 12/07/1979), Reynaldo de Barros (12/07/1979 to 13/05/1982), Salim Curiati (13/05 / 1982 to 13/05/1983),
Jânio Quadros (1986 to 1988), Paulo Maluf (1993 to 1996) and Celso Pitta (1997 to 1999) were classified as “right-wing.” “Left-wing” mayors
were those belonging to the opposition to the military regime – the MDB – and their descendants after the political opening: Mario Covas
(13/05/1983 to 31/12/1985) and Luiza Erundina (1989 to 1992), who belonged to the PMDB and the PT, respectively.
26 | Volume 35 | Issue 2 | insna.org
Connections
Oligarchies as “Rich Club” Networks
felt that they were still not fully included in a planning
process now dominated by the Metropolitan Planning
Organizations (MPOs) also created by ISTEA. Of the two
cities, Chicago groups were more successful in getting
their MPO to be responsive to their input.
5. Comparison of the Networks
As indicated in Table 1, the policy networks vary
significantly across the three cities. The São Paulo
networks are much larger than the U.S. networks, but
also much sparser (e.g., less dense). Since density often
declines as networks become larger, this is not surprising.
As the comparison of the “strong” and “weak” tie networks
in Chicago and L.A. suggests, density is also a reflection
of the kinds of social relations elicited by interviews and
surveys. If you ask people to specify only the people they
work with closely (“strong ties”) then you will generate
a sparser network than if you ask them whom they have
worked with (“weak ties”). The differences between the
networks indicate that it is important to exercise caution
when making comparisons, since many network measures
are sensitive to the size and density of the network. In
the analysis that follows, we attempt to normalize our
measures where possible.
5.1 The Rich-Club Coefficient
When we look at the distribution of the rich-club
coefficient as a function of degree (Figures 1 and 2),
we can see that all the policy networks show a rich-club
pattern. According to Zhou and Mondragón’s (2004)
definition, rich nodes are those with the highest degrees
(much larger than the average degree). The figures
show that the people with the highest degree are also
interconnected with each other--the higher the degree, the
greater the rich club coefficient.11
Table 1: Degree, Clustering and Mixing Properties
Dataset
São Paulo
Reynaldo
Number Number Average Maximal
Density of Nodes of Ties
Degree
Degree
Shortest Path
Length Between
Nodes
Clustering
Coefficient
Assortative
Coefficient
0.030
162
429
5.3
42
3.18
0.279
-0.23
Covas
Janio
Erundina
Maluf
Pitta
0.028
0.024
0.026
0.028
0.028
198
236
209
196
204
562
686
584
551
586
5.67
5.81
5.59
5.62
5.75
47
51
49
49
49
3.23
3.32
3.37
3.24
3.25
0.299
0.286
0.312
0.321
0.305
-0.196
-0.169
-0.179
-0.191
-0.175
Chicago
Chicago – Weak
Chicago – Strong
0.403
0.106
35
33
240
63
13.71
3.82
29
9
1.62
2.91
0.62
0.413
-0.16
-0.013
Los Angeles
LA – Weak
LA – Strong
0.359
0.156
37
38
239
103
12.92
5.42
29
12
1.69
2.49
0.519
0.274
-0.114
0.006
11 MISSING FOOTNOTE
insna.org | Issue 2| Volume 35 | 27
Figure 3: Degree distribution: São Paolo networks
Figure 2: Rich Club Coefficient as a Function of Degree: Chicago and LA
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28 | Volume 35 | Issue 2 | insna.org
Figure 1: Rich Club Coefficient as a Function of Degree: São Paolo
Figure 4: Degree distribution: Chicago and LA networks
Oligarchies as “Rich Club” Networks
Oligarchies as “Rich Club” Networks
5.2 Mixing Properties
Table 1 also shows the findings for the assortative
coefficient and several other related measures.12 With
the exception of the Los Angeles strong tie network, all
the networks are disassortative (r < 0). This means that
nodes with dissimilar degree tend to be connected to each
other, i.e. well-connected nodes tend to be connected
to poorly-connected nodes and vice-versa (Zhou and
Mondragón, 2007; Colizza et al, 2006). In the case of São
Paulo, it is interesting to note that the Reynaldo regime is
the most disassortative (r = -0.230), which is consistent
with Marques’s finding that a hegemonic group is first
established during this administration. The disassortative
coefficients, however, are quite similar across the
different administrations in São Paulo, regardless of their
ideological inclination. This finding is consistent with the
argument that the hegemonic group, once established, is
quite stable (Marques 2003).
5.3 Degree Distribution
We can also contrast the São Paulo networks with
the US networks by looking at degree distribution in
these networks. The degree distribution is indicative
of a network’s global connectivity, although different
properties/mixing patterns may be found in networks
sharing the same degree distribution (Zhou and
Mondragón, 2007). One important type of degree
distribution is a “power law” distribution, in which many
nodes have only a few links and a small number of nodes
have a very large number of links (Zhou and Mondragón,
2007).
When we look at Figures 3, we see the degree
distributions approximate a power law, where there are
few nodes with a large number of connections, but most
nodes have few connections. Compared with the Chicago
and LA networks (Figure 4), the São Paulo networks
more closely resemble a power law distribution.
6. Analysis
Four bases of comparison are presented by our three
urban policy networks. The São Paulo data allows us
to examine regime-level properties over time — across
different municipal administrations. The Chicago and
Los Angeles data allow us to compare policy network
regimes in two different American cities, while holding
Connections
policy sector constant. The Chicago and Los Angeles
data also allows us to compare weak and strong tie
networks within each city (and, to some degree, to draw
generalizations about the character of weak and strong
ties in both cities). Finally, we can cautiously contrast a
Brazilian urban policy network against U.S. urban policy
networks.
All three policy networks show some tendencies
towards oligarchical organization. All of them demonstrate
a “rich-club” organization, where the best-connected
individuals or organizations are connected to other wellconnected people and groups. With the exception of the
Los Angeles strong tie network, however, all the networks
are disassortative, meaning that the well-connected are
also connected to the less well-connected. This is to be
expected in an oligarchic network, where the inner elite
collectively intermediate the social network as a whole.
While all these networks may have oligarchical tendencies,
the São Paulo networks are more clearly oligarchical than
either of the American networks. The São Paulo networks
are more disassortative than the American networks,
particularly the strong tie networks. This means that
the São Paulo elite has strong links to the entire policy
network, while elites in the American networks are less
broad-based. To some degree, this makes us reflect upon
the concept of oligarchy we have embraced. Is a regime
more oligarchical if the elite (e.g., the well-connected)
organize the broader network or ignore it? In the
Michelsian tradition, the former qualifies, but we might
consider whether the latter case also represents a form
of oligarchy. The fact that the strong tie networks in the
American cities are less disassortative than the weak tie
networks suggest that when it comes to the closest ties,
the American networks are more clubbish.
There is another more important reason, however,
to question the oligarchical qualities of the American
networks. The well-structured power law distribution
of the São Paulo networks indicates that there is a small
“inner circle” that monopolizes most of the network. By
contrast, in the American cities, this “inner circle” is not
well differentiated. In the weak tie networks, in particular,
a rather large group of institutions are well-connected,
suggesting more of a pluralist than an oligarchical regime.
In other words, there are well-connected organizations but
no small group of elite that monopolize ties. The strong
tie networks appear closer to power law distributions,
suggesting a more distinct elite. But even these networks
do not differentiate between a small well-connected elite
12 Each of the São Paulo networks contains multiple components. In the rich club analysis, we only considered the giant component, which is
the largest component in a network. The giant component contains more than 90% of the nodes in these networks. All other analyses consider
entire networks.
insna.org | Issue 2| Volume 35 | 29
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and a less well-connected periphery.
Our analysis concludes that the São Paulo
networks come much closer to being oligarchies than do
the American networks. While the American networks
have some oligarchical tendencies, they ultimately
appear more pluralistic. Well-connected organizations
in the American networks are clubbish, but the analysis
does not suggest that this elite is very well differentiated.
Without studying other Brazilian cities, it is difficult
to confidently conclude that these contrasts represent
national differences in urban policy networks. But the
contrast suggests that this is a distinct possibility. One
thing that is clear from the data, however, is that the
Brazilian oligarchy appears to be stable across municipal
administrations, a point that reinforces the argument
made by Marques (2003) about these networks. Different
political parties were in charge during these different
administrations, so it is striking to find this stability. There
is a sharp disjuncture in the distribution of the rich-club
coefficient at higher degrees during the first left-wing
administration (Covas) that probably reflects an attempt
to destabilize the oligarchy. But the distribution returns to
the prior pattern under the next left-wing administration
(Erundina).
The contrast between Chicago and Los Angeles
was less striking than we anticipated, though in the
expected direction. As mentioned, Los Angeles is reputed
to be a civically fragmented city, while Chicago has a
reputation for more civic cohesion. The distribution of
the rich-club coefficient by degree (Figure 2) is very
similar: in both cities, the well-connected are strongly
linked to one another. The Los Angeles networks are less
disassociative than the Chicago networks, suggesting
that that the well-connected organizations in Los Angeles
are less well-connected to the wider network. This could
be one indicator of greater fragmentation in the Los
Angeles networks. For the strong tie networks, Chicago
also appears somewhat closer to a power law distribution
(many organizations with few ties; a few organizations
with many ties) than the Los Angeles network; in Los
Angeles, many organizations have a medium range of
ties. Our conclusion is that there is a less distinctive elite
in Los Angeles. For the weak tie networks, however, this
contrast is less clear.
Oligarchies as “Rich Club” Networks
the precise meaning of the concept is often suggestive
rather than precise. In this paper, we provide a structural
analysis of the concept based on social network analysis.
Building on the classic treatment of oligarchy by
Michels, we begin with a conception of oligarchy as a
social structure organized and dominated by a small
inner circle of prominent actors tightly interconnected
among themselves. These “oligarchs” are linked to less
prominent actors in the network, who are only weakly
interconnected among themselves. The power of an
oligarchy lies in the cohesion of the oligarchs, their ability
to organize less prominent actors, and the weakness of
these less prominent actors to organize themselves.
Our main contribution is to operationalize this idea using
a “rich club” approach. The social network concept of a
“rich club” captures the idea that well-connected actors
(high degree) are also connected among themselves.
The “mixing properties” of a rich-club network indicate
whether well-connected actors are only connected to
each other (assortative) or to less well-connected actors
(disassortative). Finally, by evaluating whether the
network fits a power law distribution (few actors of high
degree; many actors of low degree), we can determine
whether the inner-circle is a small or large group relative
to the size of the network.
We demonstrate the efficacy of this approach by
analyzing and comparing several urban networks. Our
analysis of São Paulo, Chicago, and Los Angeles suggests
that policy networks have oligarchical tendencies, in the
sense that well-connected actors in all three cities tend
to be connected to other well-connected actors. The São
Paulo networks, the weak tie networks in Chicago and
Los Angeles, and the Chicago strong tie network are
also disassortative, meaning that the well-connected
actors are connected to less well-connected actors.
However, only the São Paulo networks demonstrate a
clear power law distribution, indicating a small coterie
of well-connected actors. We conclude that the São Paulo
networks come closest to being oligarchical regimes,
while the Chicago and Los Angeles networks are more
pluralist. Remarkably, the oligarchical structure of the
São Paulo networks is stable across several municipal
administrations, suggesting that oligarchy, once formed,
may be a robust form of political organization.
7. Conclusion
The concept of oligarchy has an illustrious history in
the social sciences, but is only weakly developed as
an analytical concept. Though it is not uncommon to
hear the word used to describe political and economic
regimes in organizations, social movements, and nations,
30 | Volume 35 | Issue 2 | insna.org
References
Arbesman, S. and Christakis, N. (2010). Leadership
Insularity: a New Measure of Connectivity
between Central Nodes Networks. Connections,
30 (1), 4-10.
Oligarchies as “Rich Club” Networks
Acemoglu, D. (2008). Oligarchic Versus Democratic
Societies. Journal of the European Economic
Association, 6, 1, 1-44.
Amaral, L. A. N., & Guimera, R. (2006). Complex
networks: Lies, damned lies and statistics. Nature
Physics, 2(2), 75-76.
Barbasi, A. L. and Reka A. (1999). The Emergence of
Scaling in Random Networks. Science, 286, 509512.
Bichir, R. (2005). Investimentos viários de pequeno
porte no município de São Paulo: 1975-2000.
In: Marques, E. and H. Torres (eds.). São Paulo:
segregação, pobreza e desigualdade sociais. São
Paulo: Editora Senac.
Borgatti, S. and Everett, M. (1999). Models of CorePeriphery Structures. Social Networks, 21, 375395.
Borgatti, S.P., Everett, M.G. and Freeman, L.C. (2002).
Ucinet for Windows: Software for Social Network
Analysis. Harvard, MA: Analytic Technologies.
Breiger, R. L. (1979). Toward an Operational Theory of
Community Elite Structures. Quality & Quantity
13(1), 21-57.
Burt, R. S. (2005). Brokerage and closure: An introduction
to social capital. Oxford University Press.
Cole, R., & Weiss, M. (2009). Identifying organizational
influentials: Methods and application using
social network data. Connections, 29(2), 45-61.
Colizza, V., Flammini, A., Serrano, M.A. and Vespignani,
A. (2006). Detecting Rich-Club Ordering in
Complex Networks. Nature Physics, 2: 110-115.
Dahl, Robert. 1961. Who Governs: Democracy and
Power in an American City. New Haven: Yale
University
Domhoff, G. W. (1967). Who Rules America? Englewood
Cliffs, N. J.: Prentice-Hall.
Everett, M. G. and Borgatti, S.P. (1999). Peripheries of
Cohesive Subsets. Social Networks, 21, 397-407.
Everett, M. G. and Borgatti, S.P. (1998). Analyzing
Clique Overlap, Connections, 21(1), 49-61.
Gould, R. V., & Fernandez, R. M. (1989). Structures of
mediation: A formal approach to brokerage in
transaction networks. Sociological methodology,
89-126.
Guriev, S. and Rachinsky, A. (2005). The Role of
Oligarchs in Russian Capitalism. Journal of
Economic Perspectives, 19(1), 131-150.
Hunter, Floyd. 1953. Community Power Structure: A
Study of Decision Makers.
Leach, D. K. (2005). The Iron Law of What Again?
Conceptualizing Oligarchy Across Organizational
Forms. Sociological Theory, 23(3), 312-337.
Connections
Lipset, S. M., Trow, M. and Coleman, J.S. (1956).
Union Democracy: The Internal Politics of the
International Typographical Union. New York:
The Free Press.
Luo, F., Li, B., Wan, X-F. and Schuermann, R.H.
(2000). Core and Periphery Structures in Protein
Interaction Networks. BMC Bioinformatics,
10(Suppl 4), S8, 1-11.
Marques, E. and Bichir, R. (2001).Investimentos públicos,
infra-estrutura urbana e produção da periferia em
São Paulo. In: Espaço & Debates, Ano XVII,
2001, nº 42.
Marques, E. (2000). Estado e redes sociais:
permeabilidade e coesão nas políticas urbanas
no Rio de Janeiro. Rio de Janeiro: Revan/Fapesp.
Marques, E. (2003). Redes Sociais, instituições e atores
políticos no governo da cidade de São Paulo.
São Paulo: Ed. Annablume.
Marques, E. (2008). “Social Networks and Power in the
Brazilian State: Learning from Urban Policies.”
Revista Brasileira de Ciências Sociais. Vol.
3, Special Edition, 14-41. Also available at:
http://www.centrodametropole.org.br/t_bb_art.
html#nome
Marques, E. (2012). Public policies, power and social
networks in Brazilian urban policies. Latin
American Research Review, Vol. 47 (2).
McAuley, J. J., da Fortoura Costa, L. and Caetano, T.S.
(2007). The Rich-Club Phenomenon across
Complex Network Hierarchies. Applied Physics
Letters 91, 084103.
Mills, C. Wright. 1956. The Power Elite. Oxford: Oxford
University Press.
Mizruchi, M. S. (1996). What do Interlocks Do? An
Analysis, Critique, and Assessment of Research
on Interlocking Directorates. Annual Review of
Sociology, 22, 271-298.
Newman, M. E. (2004). Detecting community structure
in networks. The European Physical Journal
B-Condensed Matter and Complex Systems,
38(2), 321-330.
Newman, M.E.J. (2002). Assortative Mixing in Networks.
Physical Review Letters, 89(20), 1-4.
Mondragón, R. and S. Zhou. (2012). Random networks
with given rich-club coefficient. European
Physical Journal B: Condensed Matter and
Complex Systems, 85(328), 1-6.
Obstfeld, D. (2005). Social networks, the tertius iungens
orientation, and involvement in innovation.
Administrative science quarterly, 50(1), 100130.
Opsahl, T., V. Colizza, P. Panzarassa and J. J. Ramasco.
insna.org | Issue 2| Volume 35 | 31
Connections
(2008). Prominence and Control: The Weighted
Rich-Club Effect. Physical Review Letters, 101,
168702.
Polsby, N.W. (1960). How to Study Community Power:
The Pluralist Alternative. The Journal of Politics,
22(3), 474-484.
Simmel, G. 1950. The Sociology of Georg Simmel. Simon
and Schuster.
Stovel, K., & Shaw, L. (2012). Brokerage. Annual Review
of Sociology, 38, 139-158.
Voss, K. and Sherman, R. (2000). Breaking the Iron
Law of Oligarchy: Union Revitalization in the
American Labor Movement. The American
Journal of Sociology, 106(2), 303-349.
Wasserman, S. and Faust, K. (1994). Social Network
Analysis: Methods and Application. Cambridge:
Cambridge University Press.
Watts, Duncan. 1999. Small Worlds: The Dynamics of
Networks Between Order and Randomness.
Princeton: Princeton University Press.
Weir, M., Rongerude, J. and Ansell, C. (2009).
Collaboration is not enough: Virtuous Cycles of
Reform in Transportation Policy. Urban Affairs
Review, 44(4), 455-489.
Zhou, S. and Mondragón, R. (2004). The Rich-Club
Phenomenon in the Internet Topology. IEEE
Communications Letters, 8(3), 180-182.
Zhou, S. and Mondragón, R. (2004b). Redundancy and
robustness of the AS-level Internet topology and
its models. IEE Electronic Letters, 40(2), 151152.
Zhou, S. and Mondragón, R. (2007). Structural constraints
in complex networks. New Journal of Physics,
9(173), 1-11.
Zhou, S. (2009). Why the Internet is so ‘small’? LNICST,
16, 4-12.
32 | Volume 35 | Issue 2 | insna.org
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