The Romanian social fractal.
Cosoi, Alexandru Catalin ; Cosoi, Carmen Maria ; Sgarciu, Valentin 等
1. INTRODUCTION
A meme is a unit or element of cultural ideas, symbols or
practices; such units or elements transmit from one mind to another
through speech, gestures, rituals, or other imitable phenomena. The
etymology of the term relates to the Greek word mimema for mimic. Memes
act as cultural analogues to genes in that they self-replicate and
respond to selective pressures.
Blogosphere is a collective term encompassing all blogs and their
interconnections. It is the perception that blogs exist together as a
connected community (or as a collection of connected communities) or as
a social network.
A meme-tracker is a tool for studying the migration of memes across
a group of people. The term is typically used to describe websites that
either analyze blog posts to determine what web pages are being
discussed or cited most often on the World Wide Web, or allow users to
vote for links to web pages that they find of interest.
The introduction of meme-trackers was instrumental in the rise of
blogs as a serious competitor to traditional printed news media. Through
automating (or reducing to one click) the effort to spread ideas through
word of mouth, it became possible for casual blog readers to focus on
the best of the blogosphere rather than having to scan numerous
individual blogs. The steady and frequent appearance of citations of or
votes for the work of certain popular bloggers also helped create the
so-called "A List" of bloggers.
The PostRank (www.postrank.ro) project started around the first
half of 2008 as the first memetracker for the Romanian blogosphere. The
main feature for classification applied by PostRank was influence.
Further on, we must now define what influence is. Alex Mucchielli
defined it as an ensamble of manipulation procedures of the cognitive
objects which defines the situation.
The Yale approach specifies four kinds of processes that determine
the extent to which a person will be persuaded by a communication.
* Attention: One must first get the intended audience to listen to
what one has to say.
* Comprehension: The intended audience must understand the argument
or message presented.
* Acceptance: The intended audience must accept the arguments or
conclusions presented in the communication. This acceptance is based on
the rewards presented in the message.
* Retention: The message must be remembered, have staying power.
The Yale approach identifies four variables that influence the
acceptance of arguments.
* Source: What characteristics of the speaker affect the persuasive
impact?
* Communication: What aspects of the message will have the most
impact?
* Audience: How persuadable are the individuals in the audience?
* Audience Reactions: What aspects of the source and communication
elicit counter arguing reactions in the audience?
The main distance used in PostRank for top30 is Influence =
Acceptance X Retention. (FocusBlog, 2008).
2. PROPOSED METHOD
Scale-free graphs represent a relatively recent investigation topic
in the field of complex networks. The concept was introduced by Albert
and Barabasi in order to describe the network topologies in which the
node connections follow a power law distribution. Common examples of
such networks are the living cell (network of chemical substances
connected by physical links). Although traditionally large systems were
being modeled using the random graph theory developed by Erdos and Renyi
(On random graphs), during the last few years research has lead to the
conclusion that a real network's evolution is governed by other
laws: regardless of the network's size, the probability P(k) that a
node has k connections to other nodes is a power law:
P(k) = [ck.sup.-[gamma]] (1)
This implies that large networks follow a set of rules in order to
organize themselves in a scale-free topology. Barabasi and Albert show
the two mechanisms that lead to this property of scale invariance:
growth (continuously adding new nodes) and preferential attachment (the
likelihood of connecting to existing nodes which already have a large
number of links). Therefore, scale-free networks are dominated by a
small number of highly connected hubs, which on one hand gives them
tolerance to accidental failures, but on the other hand makes them
extremely vulnerable to coordinated attacks.( Barabasi and
Albert--Statistical mechanics of complex networks)
Based on the remark that random graph-theory does not explain the
presence of a power law distribution in scale-free networks, Barabasi
and Albert (2002) recommend a growth algorithm that has this property.
They show that the assumptions on which the models have been generated
up to that point were genuinely false: firstly, considering the number
of nodes as being fixed and constant and secondly, the fact that
connections were randomly established between the nodes. In fact, real
networks are open systems, continuously evolving by adding new nodes.
(Ursianu &Sandu, 2007).
As opposed to a random graph, in which all nodes have approximately
the same degree, a scale-free graph contains a few so-called hubs (nodes
with a great number of links, like the Britney Spears Twitter Profile
with 867333 followers), while de majority of the nodes only have a few
connections (50% of the twitter users have an average of 10
connections): this is a power law distribution. In a random network the
nodes follow a Poisson distribution with a bell shape, and it is
extremely rare to find nodes that have significantly more or fewer links
than the average. A power law does not have a peak, as a bell curve
does, but it is instead described by a continuously decreasing function.
When plotted on a double-logarithmic scale, a power law is a straight
line. (Ursianu & Sandu, 2007).
There are two major ways to compute the dimension of this network:
box counting method and the cluster growing method.
For the box counting method, let NB be the number of boxes of
linear size [l.sub.B], needed to cover the given network. The fractal
dimension [d.sub.B] is then given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
This means that the average number of vertices <[M.sub.B]
([l.sub.B])> within a box of size [l.sub.B]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
By measuring the distribution of N for different box sizes or by
measuring the distribution of <[M.sub.B] ([l.sub.B])> for
different box sizes, the fractal dimension [d.sub.B] can be obtained by
a power law fit of the distribution.
For the cluster growing method, one seed node is chosen randomly.
If the minimum distance l is given, a cluster of nodes separated by at
most l from the seed node can be formed. The procedure is repeated by
choosing many seeds until the clusters cover the whole network. Then the
dimension [d.sub.f] can be calculated by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where <[M.sub.c]> is the average mass of the clusters,
defined as the average number of nodes in a cluster. These methods are
difficult to apply to networks since networks are generally not embedded
in another space. In order to measure the fractal dimension of networks
we need the concept of renormalization.
In order to investigate self-similarity in networks, we use the
box-counting method and renormalization. For each size [l.sub.B], boxes
are chosen randomly (as in the cluster growing method) until the network
is covered, A box consists of nodes separated by a distance l <
[l.sub.B]. Then each box is replaced by a node (renormalization). The
renormalized nodes are connected if there is at least one link between
the un-renormalized boxes. This procedure is repeated until the network
collapses to one node. Each of these boxes has an effective mass (the
number of nodes in it) which can be used as shown above to measure the
fractal dimension of the network.
The fractal properties of the network can be seen in its underlying
tree structure. In this view, the network consists of the skeleton and
the shortcuts. The skeleton is a special type of spanning tree, formed
by edges the having the highest betweenness centralities, and the
remaining edges in the network are shortcuts. If the original network is
scale-free, then its skeleton also follows a power-law degree
distribution, where the degree can be different from the degree of the
original network. For the fractal networks following fractal scaling,
each skeleton shows fractal scaling similar to that of the original
network. The number of boxes to cover the skeleton is almost the same as
the number needed to cover the network. (Ursianu &Sandu, 2007).
In order to establish whether these networks are indeed scale-free,
we determined the degree-distribution P(k), which is the probability of
finding a node with a degree k in the Romanian Blogosphere. The obtained
distribution is indeed scale-free and satisfies the power law with the
exponential: [gamma] = 2.65 which satisfies our condition to be between
2 and 3.
P(k) [approximately equal to] [ck.sup.-[gamma]] (5)
logP(k)) = (-[gamma])log(k) + log(c) (6)
y = (-[gamma])x + c (7)
By using the box counting method, weobtained the dimension
[d.sub.B] = 2.72. This means that this network is indeed a fractal
network.
On this level of influence we can find both influent bloggers and
also random blogs wich hope to increase their visibility by approaching
subjects similar to influent bloggers.
In Romania, blogging is still in an incipient state. There are
still just a few highly influent blogs, and the approached post are on
similar subjects--news and online businesses.
3. CONCLUSIONS
Several fundamental properties of real complex networks, such as
the small-world effect, the scale-free degree distribution, and recently
discovered topological fractal structure, have presented the possibility
of a unique growth mechanism and allow for uncovering universal origins
of collective behaviors. However, highly clustered scale-free network,
with power-law degree distribution, or small-world network models, with
exponential degree distribution, are not self-similarity.
We believe that analyzing the fractal properties of the Romanian
Blogosphere will give us an insight of the future Citizen Journaling and
its influence in the local media. Even though at its beginning, influent
bloggers are already present and will increase their influence in time
and create other Class A bloggers, and this will cause the network to
keep expanding.
4. REFERENCES
Albert, R., Barabasi A., Statistical mechanics of complex networks.
Review of modern phishics 47-97.
Bausch, S., McGiboney, M. Media Alert. Nielsen-Online (Available
from: www.nielsen-online.com).
Dawkins, R. The selfish gene. ISBN 0199291144, 9780199291144,
Published by Oxford University Press, 2006
Erdos, P., Renyi A., On random graphs. Publ Math. Inst. Hung. Acad.
Sci, 290-297.
MacManus, R. The Fractal Blogosphere. (Available from:
http://www.readwriteweb.com/ about_readwriteweb.php Accessed on :
2009-03-14).
Shirky C. (2003). Power Laws, Weblogs, and Inequality. In: Clay
Shirky's Writings About the Internet--Economics & Culture,
Media & Community, Open Source
Thompson, C. The Haves and Have-Nots of the Blogging Boom. New York Magazine (Available from: http://nymag.com/news/media/15967/, Accessed
on : 2009-03-14).
Ursianu, R., Sandu A., Self-Similarity of scale-free graphs.
Proceesings of CSCS 16, Bucharest, Romania, page 121.
Zou, L., Pei W, Li T., He Z., Cheung Y. (2006). Topological fractal
networks introduced by mixed degree distribution. In: Data Analysis,
Statistics and Probability
Yale attitude change program. Persuasive communication theories of
persuasion and attitude change. (Available
from:www.elcamino.edu/faculty/rwells/PERSUASIVE%20 COMMUNICATION.ppt,
Accessed on:2009-04-01).
***FocusBlog (a Romanian BlogoSphere Memetracker, Available from:
www.focusblog.ro).