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).