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Review of Sociology Vol. 9 (2003) 2. 151–159
THE NETWORK SAGA*
Budapest University of Economic Sciences and Public Administration
Budapest, Fõvám tér 8. H-1093; e-mail: email@example.com
Barabási, Albert-László: Linked. The New Science of Networks.
Cambridge MA: Perseus
A Hungarian sociologist has two good reasons to be proud nowadays.
First, as a Hungarian, since on the other side of the ocean a Hungarian book has
become a real hit. Considered a scientific bestseller “Linked” can be thought of as ahundred per cent Hungarian, not only due to the author’s Hungarian origin, but also,because the book offers a wide spectrum of Hungarian-related information.
On the other hand, for a sociologist it is of no little consequence that finally – after a
century during which it was predominantly the area of natural sciences that served as asource of inspiration for social sciences – a reverse process has been witnessed. Thetheoretical and methodological results of social network analysis
– basically adiscipline of sociology/anthropology – are now the focus of natural sciences.
Barabási’s book deals with familiar questions in the fields of economy and sociology,but beyond that it examines a number of examples from the areas of physics,information sciences and cell biology where network analysis is the key to makingfurther progress.
Obviously, it is not the Hungarian connections, nor the implications in the area of
social sciences to which Linked
owes its international success. Rather, the fact is thatthe book was capable of presenting the recent and significant challenges of modernscience in an intriguing, non-technical language, in the manner of a real page-turner.
This book is a popular scientific summary of the author’s earlier publications – and it isalso the first book about network analysis to warrant widespread public attention.
The present review aims at not only expounding on the book, but to showing its
international reception, partly based on an interview with the author.
This review has been translated by Kata Erdõdi.
1417-8648 2003 Akadémiai Kiadó, Budapest
The slogan-like subtitle on the cover of the book invites us to read and learn “how
everything is connected to everything else and what it means for science, business andeveryday life”. A review published in New Scientist
(Cohen 2002) claims that a singlelaw has been discovered that simultaneously applies to our sexual life, the functioningof proteins and the world of movie stars.
This “omnipotent” law is the scale-freemodel.
The concept of the scale-free network was previously published by Albert-László
Barabási and his research group (Réka Albert and Hawoong Jeong) in a number ofpapers. The article that appeared in Science
in 1999 became the most cited paper in thearea of physics in the United States in the year 2002. The paper dealing with theauthors’ insights on the attack
and error tolerance
of Internet and modern economywas published in 2000, making it a Nature cover story. Success encouraged Barabási towrite further papers and finally a book that was meant to convey the message to all:think network.
The message of the book can be summed up briefly. Earlier, following in the wake
of Paul Erdõs and Alfred Rényi, graph theory dealt with the examination of random
connections where the number of links belonging to each node follow a Poissondistribution. Barabási points out that in systems that evolve without regulation, in anatural way the connections are not random. On the contrary, the new arrivals areprone to link themselves to previously formed, highly connected hubs (cf. “networkdependent path dependence” Sik 2003). For this reason most of the networks found innature and in society are characterized by a power law, rather than a Poissondistribution. In order to demonstrate the difference between networks with Poisson andpower law degree distributions, Barabási uses a number of ingenious examples. Ofthese I will present the comparison of the highway map and the air traffic system in theUnited States. “On the roadmap cities are the nodes and the highways connectingthem the links. This is a fairly uniform network: Each major city has at least one link tothe highway system, and there are no cities served by hundreds of highways. Thus mostnodes are fairly similar, with roughly the same number of links. (…) Such uniformity isan inherent property of random networks with a peaked degree of distribution.
The airline routing map differs drastically from the roadmap. The nodes of this
network are airports connected by direct flights between them. Inspecting the mapsdisplayed in the glossy flight magazines placed on the back of each airplane seat, wecannot fail to notice a few hubs, such as Chicago, Dallas, Denver, Atlanta, New York.
(…) The vast majority of airports are tiny, appearing as nodes with at most a few linksconnecting them to one or several hubs. Thus, in contrast to the highway map, wheremost nodes are equivalent, on the airline map a few hubs connect hundreds of smallairports”
(Barabási 2002: 6th link/2).
Consequently, based on the argument above, the scale-free model can be defined:
“Power laws mathematically formulate the fact that in most real networks the majorityof nodes have only a few links and that these numerous tiny nodes coexist with a fewbig hubs, nodes with an anomalously high number of links.
In a random network the peak of the distribution implies that the vast majority of
nodes have the same number of links and that nodes deviating from the average areextremely rare. Therefore, a random network has a characteristic scale in its nodeconnectivity, embodied by the average node and fixed by the peak of the degreedistribution. In contrast, the absence of a peak in a power-law degree distributionimplies that in a real network there is no such thing as a characteristic node. We see acontinuous hierarchy of nodes, spanning from rare hubs to the numerous tiny nodes.
The largest hub is closely followed by two or three somewhat smaller hubs, followed bydozens that are even smaller, and so on, eventually arriving at the numerous smallnodes.
The power law distribution thus forces us to abandon the idea of a scale, or a
characteristic node. (…) There is no intrinsic scale in these networks. This is the
reason my research group started to describe networks with power-law degree
distributions as scale-free”
(Barabási 2002: 6th link/2).
Barabási first discovered the existence of scale-free networks when investigating
how the World Wide Web functions. While examining how websites are connected toone another by links,
he realized that the World Wide Web is composed of very fewcentral and a vast number of peripheral websites. Such a construct could evolve,because the World Wide Web is a system where growth is not regulated and wheremost of the new websites are linked to already existing, in fact, already well-knownand therefore important websites.
The author’s extraordinary achievement is that he could “think outside the box”
and cross the frontiers of information sciences – his research field in the strict sense –to collaborate with physicists, biologists and many others. In the book one may findseveral examples that show how all of a sudden the scale-free model provides asolution to many unsolved mysteries of modern science. While the cell biologists’main concern was trying to determine the components and the functions of proteins,Barabási and Zoltán Oltvai tried to shed light on the functioning of proteins byexamining how these components are connected. They stated that “each cell lookedlike a tiny web, extremely uneven, with a few molecules involved in the majority ofreactions – the hubs of the metabolism – while most molecules participated in only oneor two”
(Barabási 2002: 13th link/3). The cell’s scale-free structure may be theconsequence of its non-regulated evolution: “to be sure, the original assembly of thefirst protocells from a primordial soup of organic molecules might have resembled agrowing network”.
Based on the results of research conducted in several countries, Barabási points out
that the network of sexual relationships
is also scale-free: contemporary society ismade up of a great number of people who had had very few sexual relationships and afew who had had extremely many. Consequently, with regard to the AIDS epidemicand other sexually transmitted diseases the author makes a simple, but no doubtshocking suggestion: “…Hubs play a key role in these processes. Their unique rolesuggests a bold but cruel solution: As long as resources are finite we should treat onlythe hubs. That is, when a treatment exists but there is not enough money to offer it toeverybody who needs it, we should primarily give it to the hubs. This was theconclusion reached in two recent studies, one by Pastor-Satorras and Vespignani, the
other by Zoltán Dezsõ, a graduate student in my research group. (…) Any selectivepolicy raises important ethical questions. Indeed, our results indicate that, faced withlimited resources, we would end up rewarding promiscuity. (…) Are we ready to offerdrugs to the more connected poor prostitutes than to the wealthier but sexually lessconnected middle class?”
(Barabási 2002: 10th link/10)
Further examples range from the world of the movies to business and
microelectronics and apparently support what Barabási himself wrote about the
reception of their insights: “With the realization that most complex networks in nature
have a power-law degree distribution, the term scale-free networks rapidly infiltrated
most disciplines faced with complex webs”
(Barabási 2002: 6th link/2).
In addition to discovering the significance of scale-free networks, Barabási and his
research group were also interested in mapping the characteristics of scale-free
systems. Their most important findings concern the robustness
of the system. “Node
failures can easily break a network into isolated, noncommunicating fragments. (…) A
significant fraction of nodes can be randomly removed from any scale-free network
without its breaking apart. The unsuspected robustness against failures is that
scale-free networks display a property not shared by random networks. As the
Internet, the World Wide Web, the cell, and social networks are known to be scale-free,
the results indicate that their well-known resilience to errors is an inherent property of
(Barabási 2002: 9th link/2). Basically robustness means that the
system is able to function with a few highly connected centers, even if the greater part
of its elements experience random failure. On the contrary, however these systems are
vulnerable to deliberate attacks,
the elimination of a few of these centres will cause
immediate breakdown and the system will fall to pieces. Barabási had shown that
among others society and the human body are also scale-free networks and he now
debates whether this is “good news for the people who depend on them.”
David Cohen (2002) claims that the discovery of the scale-free model, moreover
the understanding of the characteristics of the scale-free system will transform the waywe look at the world. As for myself, I am unable to judge whether these findings arerevolutionary.
All I know is that the book makes me believe they are.
THE ARRIVAL OF FURTHER MARTIANS
The American reader who after finishing György Marx’s book, The arrival of the
had indulged in the slightest hope that perhaps Hungarians were (are) not thepioneers of network analysis, surely admits defeat after reading Linked
. In the book itis made clear that the ideas of “small world” and “six degrees of separation”, two basicconcepts of network theory first appeared in a short story by Karinthy, decades beforebeing published in American scientific journals. Barabási speculates that perhapsStanley Milgram, the American scientist to whose name six degrees of separation islinked – “a child of a Hungarian father and a Romanian mother”
– might haveincidentally heard about Karinthy’s short story and its five degrees thanks to theHungarian connections. It is almost impossible to count how many Hungarians are
mentioned in the book, ranging from Erdõs and Rényi, the fathers of graph theory tothe author himself and his co-authors who discovered the importance of scale-freedistribution.
The thought that everybody and everything is Hungarian, seems at times to lead the
author astray. Without doubt it is touching to read in an American scientific work thatin the Kamra Theatre on Ferenciek Square there are good plays applauded by theaudience. But I find that when writing about synchronized clapping it is not necessaryto debate whether it is unique to Budapest or Eastern Europe. Fortunately, later on theAmerican examples serve to compensate such excesses (Barabási 2002: 4th link/1).
On the other hand, it is lamentable that in the case of certain innovations of genuine
importance there is no mention of Hungarian pioneers. To my best knowledge, mosttechnology historians, along with György Marx attribute the discovery of electronicmail, that is e-mail, to János Kemény who had used it to communicate with his wife inthe beginning of the sixties. Instead Barabási claims that “For example, e-mail wasborn when an adventurous hacker, Rag Tomlinson, working at BBN, a smallconsulting firm in Cambridge, Massachusetts, figured out how to modify file transferprotocols to carry mail messages. For a long time Tomlinson kept quiet about hisbreakthrough. When he first showed it to one of his colleagues, he warned him, “Don’ttell anyone! This isn’t what we’re supposed to be working on.” E-mail leaked out,however, and became one of the dominant applications of the early Internet.”
(Barabási 2002: 11th link/3)
When dealing with the virtual networks of Internet users, the ICQ and the SETI
programs are mentioned among others, while the WIW (Who is Who) projectdeveloped by Hungarians is not acknowledged. Although it has fewer users, it is nodoubt the first in the world to draw the graphical map of e-mail networks upon request.
Finally, one cannot help, but notice that there is no mention of the results of
Hungarian and Central-Eastern European network analysis. To name only one of suchfindings: in my opinion, the concept of “connection/relation
-sensitive pathdependency” may prove useful regarding the evolution of scale-free networks. Thisconcept is linked to Endre Sik (2003) in the international scientific literature. In thearea of network analysis, Hungary and Slovenia are the countries of the region whereserious research is done: in the latter the development of the popular Pajek networkanalysis program deserves mentioning.
In the introduction of the present review I stated that social network analysis
considered a discipline of sociology/anthropology until recently – is now the focus ofnatural sciences. This is probably true, but it is also part of the whole truth thatBarabási’s book sheds little light on this process. In this aspect I share the views ofFernard Amblard who notes, with regard to Linked
and two other books that “the factthat the authors don’t mention the contribution of sociology to the “science networks”is disappointing. Many empirical studies (in Social Networks or JOSS for instance),measures (Wasserrmann and Faust 1994) and rationales (Coleman 1990) have been
developed in network research and social capital theory but these are totally absentfrom the books reviewed.”
About Barabási’s book Amblard also remarks “a tendencyto present it in a partial way, i.e. as a physicist interested through his work in manydiverse areas but forgetting most of the time what professionals in these domains mayhave to say about networks or his findings.”
Let’s state the facts: Barabási writes about four studies in the field of sociology.
Stanley Milgram’s “small world” theory, Mark Granovetter’s thesis on the strength ofweak ties, and with regard to tetracycline and hybrid corn, the work of Bryce Ryan,Neal C. Cross, Elihu Katz, James Coleman and Herbert Menzel is presented in thebook, in an extremely entertaining way. The author cannot be blamed for not giving thereader a general overview of the development of social network analysis, because thiswas not his point. But in addition to the ones listed above, it would have been essentialto mention those social scientists who have dealt with methodological problems verysimilar to the ones Barabási faces and have important findings in this area. To nameonly a few: Franz Stokman whose research interest is network dynamics, PhilipBonacich who worked out the indicators of network centrality, Ronald Burt whoinvestigated structural holes and Linton C. Freeman who worked on the visualizationof networks.
Let’s see an example! Regarding network density and centrality (Barabási does not
use these concepts), the book cites a physics-related paper published in 1998: “Watts
and Strogatz introduced a quantity called the clustering coefficient. Let’s assume that
you have four good friends. If they are all friends with each other as well, you can
connect each of them with a link, obtaining altogether six friendship links. Chances
are, however, that some of your friends are not friends with each other. Then the real
count will give fewer than six links –let’s say, four. In this case the clustering
coefficient for your circle of friends is 0.66, obtained by dividing the number of actual
links between your friends (four) by the number of links that they could have if they
were all friends with each other (six). The clustering coefficient tells you how closely
knit your circle of friends is. A number close to 1.0 means that all your friends are good
friends with each other. On the other hand, if the clustering coefficient is zero, then you
are the only person who holds your friends together, as they do not seem to enjoy each
(Barabás 2002: 4th link/1)
In fact, the concepts and coefficients of clustering (and network density) date
further back, so that when speaking of their introduction, it applies only to the area ofphysics. The methodological paper of Philip Bonacich published in 1987, alreadydeals with the phenomenon of clustering as that of common knowledge and writesabout the different methods of its measurement in far more detail than the above citedpaper.
If there is little mention in Barabási’s work of the implications of network theory in
the field of sociology, there’s absolutely no mention of its implications in the field ofanthropology. This is surprising, because it is generally known that Radcliffe-Brownwas the first one to suggest that social scientists investigate social relations at hisinauguration as the head of the Royal Anthropological Society. Several studies link theevolution of social network analysis to social anthropology, the “Manchester School”(cf. Molina 2001). The classic work of Larissa Adler Lomnitz published in 1971, about
the role of social relations in the Chilean middle class is also absent from the book. Thearticle is as well known in the community of anthropologists as Granovetter’s paper onweak ties in the community of sociologists. It was translated into several languagesand has also been published in Hungarian (Lomnitz 1998). The Anthropack
softwaredeveloped in the beginning of the nineties for anthropologists was one of the firstprograms also capable of network analysis. One of the creators, the anthropologistSteve P. Borgatti collaborated in the development of the UCINET program later on.
This is the program that most researchers doing network analysis use nowadays.
When we met in person, I asked the author why he had disregarded the pioneers of
network theory, that is the social scientists. His answer was frank and sincere: hisknowledge of this literature had not been adequate. He also claimed that he intended tofurther his knowledge in this field, especially since he now wished to focus on thequality of relations. He wants to investigate beyond the limits of theories that assumethat each relation is of equal importance and hopes that social theories will be of help.
And finally some good news: Albert-László Barabási and Duncan Watts are
currently working on the edition of an anthology where network theory’s socialscientist pioneers and its contemporary natural scientist contributors will be equallyrepresented. The first piece – and also the motto - of the anthology will not be ascientific work, but a short story by Frigyes Karinthy written in 1929, the Chains.
In the past years three books have been published more or less simultaneously that
approach network analysis from the perspective of physics (Barabási and Zoltán 2002,Watts and Strogatz 1998 and Buchanan 2002). The scientific community received allthree books, especially Barabási’s, with great interest. It cannot be wondered that thediscourse they generated continues growing according to power function, since anever-growing network keeps adding to the relevant literature – very much in themanner of a scale-free system.
Apart from the reviews of the publishers, there are four critiques of high standard
that I know of: Amblard 2003, Cohen 2002, Eakin 2003 and Schrage 2002. Of thesethe most well known is no doubt the review published in New York Times. All of themare criticisms of high recognition that emphasize the author’s efforts to make hisresults known, not only in countless publications, but by the means of media, such asBBC, NPR, CBS, NBC, ABC and CNN.
Researchers doing network analysis received the results with more scepticism.
Understanding why network analysis, during the many decades of its evolution, neverreceived much attention from the press and now, all of a sudden, recent discoveriesoriginating from the area of physics are causing such havoc, is proving truly difficult.
On the mail lists of network analysts, such as SOCNET (English), REDES (Spanish),HUNNET (Hungarian), it was emphasized by all that the phenomenon Barabási callsscale-free model is by no means unknown to them. It has been recognized a while ago,but at the same time no one had considered it a general principle the way Barabási had.
Many scientists (such as Ivan Blanco, Valdis Krebs, Mark Handcock, Martina Morris)
stressed that networks may follow other types of distributions, not only the two(Poisson and power law) mentioned in the book.
ABEL ON THE WEB
Abel is the legendary main character of a series of novels (Abel in the Wilderness)
written by Áron Tamási, a well-known Transylvanian writer.
After finishing an exciting book, it is not surprising to become curious about the
author. I made good use of the Internet and the search engine produced Albert-LászlóBarabási’s home page in no time. The home page told the story of a versatile,interesting person. Barabási is originally from Csíkszereda and studied physics at theuniversity in Budapest, then got a Ph.D. in the U. S. and finally, after spending a fewyears earning money, returned to the university to do research on the Internet.
Although far from home, the research group he “recruited” is mainly Hungarian. He isa modern Stakhanovist of science: in 2002 he added 18 papers – that were eitherpublished and/or approved – to the palette of scientific literature, not counting the bookin question. On his home page three links can be considered personal:
my country(Transylvania), my city (Csíkszereda) and my people (the Székely
s). The originalEnglish version of Linked is dedicated to his parents in Hungarian: “Szüleimnek”.
Adler Lomnitz, L.  (1998): Komaság: kölcsönös szívességek rendszere a chilei városi
középosztályban. (Sponsorship: the system of mutual favours in the Chilean urban middleclass.) [Compadrazgo], Replika
29: 139–150. www.replika.hu
Amblard, F. (2003): Simultaning Social Networks: A Review of Three Books. JASSS
Angelusz, R. and Tardos, R. szerk. (1991): Társadalmak rejtett hálózata.
[Hidden Networks of
Societies] Budapest: Magyar Közvéleménykutató Intézet.
Barabási, A.-L. and Albert, R. (1999): Emergence of Scaling in Random Networks. Science
286: 509–512; http://www.nd.edu/~networks/Papers/science.pdf
Barabási, A.-L., Albert, R. and Jeong, H. (1999): Mean-filed Theory for Scale-free Random
272: 173 –187; http://www.nd.edu/~networks/Papers/physica.pdf
Barabási, A.-L., Albert, R. and Jeong, H. (2000): Attack and Error Tolerance in Complex
406: 387–482; http://www.nd.edu/~networks/Papers/nature_attack.pdf
Barabási, A.-L. and Dezsõ, Z. (2002): Can We Stop the AIDS Epidemic?
Bonacich, P. (1987): Power and Centrality: A Family of Measures. American Journal of
Buchanan, M. (2002): Nexus. Small Worlds and the Groundbreaking Science of Networks.
Cohen, D. (2002): All The world s a Net. New Scientist,
2338, 2002. 04. 13.
Coleman, J. S. (1990): Foundations of Social Theory.
Boston: Harvard University PressEakin, E. (2003): Connect, They Say, Only Connect. The New York Times,
2003. 01. 25.
Marx, Gy. (2000): A marslakók érkezése. Magyar tudósok, akik nyugaton alakították a 20.
[The arrival of the Martians] Budapest: Akadémiai Kiadó.
Molina, J. L. (2001): El análisis de redes sociales. Una introducción.
Schrage, M. (2002): Network Theory s NEW Match. In: Best Business Books 2001-2002,
Sik, E. (2003): Network Dependent Path Dependence. PDF State University – Higher School of
Economics Seminar ‘Sociology of Markets’,
October 31, 18-15.
Szántó, Z. és Tóth I. Gy. (1993): Társadalmi hálózatok elemzése. [Social Network Analysis],
Társadalom és Gazdaság,
Wasserman, S. and Faust, K. (1994): Social Network Analysis. Methods and Applications.
Watts, D. J. and Strogatz, S. H. (1998): Collective Dynamics of ‘Small-World’ Networks.
The home page of Albert-László Barabási http://www.nd.edu/~alb/
Magyar Könyvklub http://www.mkk.hu/leiras.jsp?bookID=178865
Social Network Department of Hungarian Sociological Association: www.socialnetwork.hu
HUNNET mail list: http://groups.yahoo.com/group/hunnet/
Journal of Connections http://www.sfu.ca/˜insna/indexConnect.htmlhttp://www.heinz.cmu.edu/project/INSNA/joss/index1.html
Journal of Social Structure http://www.heinz.cmu.edu/project/INSNA/joss/index1.html
Journal of Redes http://seneca.uab.es/antropologia/jlm/http://usuarios.tripod.es/revistaredes/
UCINET, Anthropack software: http://www.analytictech.com/
Erdõs number: http://www.acs.oakland.edu/˜grossman/erdoshp.html
The Network Analysis Manual of Robert Hannemanhttp://faculty.ucr.edu/˜hanneman/SOC157/NETTEXT.PDF
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