Мeasure of mutual influence among members of a social network

Among the factors that determine an individual's learning of new skills within a common interest group (in the local society) are: the strength of the character of the individual to be influenced by other members of the group or other groups and the individual's motivation. The first one of these two factors is analyzed here. To measure the influence that some members of a group have over others, and the individual's level of conform-ism, we use a semantical-logical analysis with quantitative output in the messages of a forum which contains a discussion about problems and innovations. We use a cluster analysis technique to find similarities and dis-crepancies among the members of the forum and classify them in this manner, revealing which of them are leaders and have influence over the others.

Recently, a new way for people to interact with each other (over the Internet) appeared that is generally known as a social network. This is a form of communication in which users can exchange photos, messages, an application or a text file. Some consider(s) it to be a new paradigm of social organization [1] in which there is not only exchange of information, but also an analysis and reinforcement of common topics. In this way, social networks not only allow their members to know each other and to share information about their activities, but also organize groups, events and offer services.

Social networks enable their members to meet people whom it would be difficult for them to meet face- to-face. Each one can produce their own content, allowing them to have professional contacts which can help businesses (to spread knowledge) and form bonds or even working groups among its members. They allow their participants to create a feeling of self-fulfillment.

1.2.     Measurements in Social Networks

As Javier Godoy says, “The problem is that we need to change the paradigms. When the Internet was a place of anonymous navigation where people came to consume content, what we were interested in measuring was the consumption of content, not who consumed it. Now, the Internet is social environments where the principal content we consumer are the users themselves, so what we are interested in measuring are the users.” [2]

In social networks there are different Key Perfomance Indicators (KPI) and some tools such as Google Analytics which allow us to gather information about the traffic on websites. Other tools such as Google Alerts or Social mention allow us to follow, via email, which appears on social networks about a topic, a business or a person. But these only let us know the general parameters of the network but not the influence that its members have over others.

There are also corporate social networks in which social network’s technology are applied within the scope of organizations to increase productivity [3]. It can help the business because it will obtain, first hand, the opinions of the users and potential clients about its products, which can be used in the creation of new products or services. On the other hand it helps the client to improve his self-fulfillment. And that in turn, gives better feedback to the business.

There are social technologies which are very close to social network’s technologies.

1.3.     Social Technology

There are many definitions of social technologies, but mostly they either belong to the parcial sector of activity, or unclear, vague. Most suitable for our study the following definitions [6]: Social technology is a set of methods and techniques to deliver results in problems of interaction between people, or social technology is the communicative structure influences that change the social system or situation. Social technologies-solutions to social problems, to shape the living conditions and development of societies, social relations, social structures in order to ensure human needs, create conditions for the realization of his potential abilities and interests, taking into account that are sanctioned by society's value system and the interdependence between social progress and economic development.

There is also the notion of Humanitarian technology: Humanitarian technology-social technology based on practical use of knowledge about a person in order to create conditions for the free and all-round development of the individual.

It is considered educational one interesting example of social technology that can be found in the history of the introduction of the potato crop to France, it is an example of an astute plan to implement an idea [5].

Antoine Augustin Parmentier, a French military pharmacist and agronomist, introduced the potato to France. Parmentier got Luis XVI to allow the potato to be planted in the outskirts of Paris, in the plains of Les Sablons, known for their infertility. Later, he got them planted in the plains of Grenelle, what is now Champ de Mars. A skillful publicity stunt allowed the definitive introduction of the planting and consumption of potatoes to be accepted by even the most doubtful people.

The farm that the King gave to Parmentier to plant with potatoes was guarded by a heavy military presence during the day, which gave the impression that what was going on there had to do with a very valuable product. But the guard was deliberately let down at night, allowing people from the surrounding area a chance to sneak in and steal the precious product from the field at night, converting that into the best advertising for the new crop. At a reception given by King Luis XVI, his majesty presented Parmentier with a bouquet of potato flowers saying, “One day France will thank you for having found the bread for it's pour.”[5]

It is known that new technologies penetrate vital activities through the achievements of natural science for example: the laws of physics allow for the development of machines and tools that can substitute for human labor. At the same time methodologies from natural sciences can assist in the development of methodologies in social sciences, which in turn, develop knowledge about human beings, society, and social wellbeing. The knowledge about social customs and about the processes in which new ideas (innovations) and paradigm can be converted into popular ideas and find a place in popular opinion as economically and socially useful, without contradiction to traditional culture.

It is known, that new paradigm is made up of three components:

-         New technologies developed by science in sufficient quantities.

-         New resources (including human resources with new skills) or resources which are not new but respond to new demands of production of technological innovation.

-         The population and specialists accepted the ideas and technologies of ершы new paradigm to follow and develop as guidelines.

For this third component, the creative group should draw up or accept from scientists, human (social) technologies to persuade citizens to accept the technological innovations. The human technologies do not reduce the training of the population. Its function is to reorganize the community, creating new social structures that can act to fulfill the new demands of the super-system and produce additional values.

Figure 1. Influence of natural sciences in vital activities.

In Figure 1 we can see that technological innovations are developed from natural sciences. It's methods help to develop social sciences and humanities. Social sciences create human technologies when the demand for them is arising for implementation of a new technical paradigm in the vital activities.

1.4.      System of equations of mutual influence in social networks or a simple model of human behavior in the enterprise

Let us consider a model of human behavior in the working group with a stable external environment (without taking into account the influence of the environment), as proposed by Krasnoschekov P.S. y Petrov A.A. (2000).

We call as the State «A» the situation where a person accepts the idea of the system (enterprise): his/her behavior is in concordance with discipline, (s)he shares the goals of the work, (s)he is interested in the outcome, is involved in the process improvement, product development and support of certain innovations or paradigms, etc. and (s)he likes to be a member of the working group.

The individual makes the decision (to accept or to reject state (status) A), in two stages: before and after an exchange of opinions with other people of enterprise, or we could say: individually or under the influence of colleagues

1.4.    Case Study of OTVETY

The site “otvety.ru” is a very popular social network (semi-network) in Russia. It has characteristics that allow us to see the level of influence that some users have over other users through questions, answers and comments. The level of influence can be evaluated by comparing the content of dialogues; one person destroys the argument of an opponent with their votes in favor or against the messages and a system of votes for questions and answers. Furthermore, it has a system of ranking of participants based on their level of activity and number of votes for them.

This system of ranking is on one hand a motivation to increase their activity and on the other hand the high rank to the author of a message influences morally the other users - massage receiver. The system has a level of defense against bad words, swearing, and lie, especially with incorrect links or advertising.

These characteristics can be found in other forums but in OTVETY they are more complete. Some of these characteristics can be used for an analysis of the mutual influence in discussions.

2.        CHARACTERISTICS OF THE FORUM “ SOCIAL AND CULTURAL ASPECTS OF THE MIXTECA” FOR THE EXPERIMENT

For the analysis of mutual influence of visitants of platforms for debate in the internet we used (created by us) forum “Social and Cultural Aspects of the Mixteca (ASCM in its Spanish initials). Forum members can make comments and propose solutions to the topics of discussion. Furthermore they can express their consent or disagreement with a comment made by other members of the forum. In the forum, topics are discussed concerning problems in the city and possible directions that would be beneficial to the city or ways for the city to obtain more resources or income. Problems relating to city traffic and transportation and ecology are also discussed.

This article we only use the data collected in the topic of transportation for our case study.

From the members of the forum we picked out one group of members who proposed different alternatives to the transportation problem. This group was divided into three: invited experts who we call “Teachers”, a second group of independent active experts “uncertain” who accept (with criticism) but... didn’t reject a priori everything, these usually proposed by the Teachers. And a third group made up of independent individual experts “independent Opinion” with their own (specific) opinions.

With their messages, we created a matrix which allows us to calculate p and 1 in relation to each one of the other members of the forum (passive experts). This matrix has a structure that logically follows from the algorithm of the calculation of p and 1.

3.          ANALYSIS AND CALCULATION OF THE COEFICIENT OF THE

CONFORMITY Ц AND THE COEFFICIENT OF MUTUAL INFLUENCE λ

We return to the system of equations (4) to create an algorithm to calculate the coefficients μ and λ from the material of the forum:

3.1.      Calculation of μ

We can do this only if the passive experts are sincere and responsible for analysis what they are produced, and not placed randomly their results of estimates. People don't change their opinion too often, so μ reflects the nature of the individual and this feature can be used with measurements in other discussions with them.

Therefore, to calculate the ц in Excel, we use the following algorithm:

-         Find words in all messages "pro state A" or "against state A" (Ā).

-         In the row below the row of messages we put a logical feature in form 1 for condition A and “-1”for condition A.

-         We ask the participants (the same as appraisers, assessors, evaluators) to express their opinion and assessment in the form of a "1" in the event of consent, "0", if their opinion is not formed, and -1 if they do not agree with the idea of the state A.

-         If the appraiser fully supports all the statements of active experts (evaluation coincides) then the appraiser is a complete a conformist and its coefficient of μ should equate to zero.

-         If the assessor does not agree with all the statements, then it's coefficient of ц is equal to 1.

-         If we compare the K pairs of estimations and there are differences among them, then ц is equal to the sum of all differences divided by K (quantity of pairs).

What changes should be made in the algorithm, if the evaluator himself expressed their opinions on each issue, which had not yet been discussed with the experts?

In this case, we can predict the behavior of the evaluator for different statements of an expert. Then we can capture only the deviations from these predictions, and they will determine the impact of active experts in the opinion of the evaluator.

3.2.          Calculation of λ

3.3.          Calculation of the initial probabilities and the coefficients

The semantic analysis of the messages of the user k, allows us to determine the amount of them in which user k:

-        Accepts State A given the arguments in favor of an idea that is discussed and developed. (State MA)

-        Does not accept the idea or State A (negates or rejects) and has doubts about it and arguments against it. (State MĀ)

-        Expresses ambiguity or confusion that does not permit an interpretation of his sentence as for or against an idea (State M0).

The last situation (case) should be excluded from the following analysis and the first two cases should be taken into account for calculating the probability of case that user k accepts state A. P(A)=amount of cases A(MA) /(sum of amounts of cases A and Ā) P(A)=sum of MA/(sum of MA + sum of MĀ)

Also P(A) could be assigned value “1” if the user, in his latest message, accepts the idea A), when argues with other members of the forum. Even if in the process of the discussion this participant with number «k” could say something against idea A, but finally accepts the idea then his decision to accept it could still influence other participants in the discussion, for example the passive participants.

This indecision of participant k should be taken in account when calculating μ.

μ= (the amount of sentences pro A)/

(the sum of the common amount of all his sentences type MA and MĀ).

Therefore through P(A) and p we can measure the influence of user k over other users in the discussion and vice versa for k-th user.

Sometimes the State A cannot be expressed in a single affirmation but it can be formulated as a group of ideas, which express a paradigm. We can have the total results of the exchanges of opinions for the different topics expressed in State A through simple sums. In this case, formula 4 could be more complete.

4.       RESULTS OF THE APLICATION OF THE DEVELOPED METHOD IN THE EVALUATION OF PARTICIPANTS IN THE FORUM ASCM

For the calculation of μ and λ for integrated experts “teacher” and for experts with independed opinions (see part 2 of present article) we accept that μ_teacher and μ _{independed_Opinion} have values of 1.

For μ_uncertain we calculated for the method provided in 3.1 and we received a value of 0.86

The application of the method to calculate p and 1 gives us the matrix presented in table 1. In which we have grouped the experts (active and passive). Each of these groups corresponds to their own row of the table. These were obtained by clustering from the matrix where we have objects (Experts) and as attributes (coefficients μ and λ for each expert). The Visual Heuristic Cluster Analysis (VHCA) method was used. [Makagonov, P. and Sboychakov, K (1998).] In the result (table 1) we have 6 groups of participants from the evaluation of the messages in the forum.

Table 1.

Group 1: 1 active participant (doubtful) and 1 passive expert

Group 2: 1 anonymous participant, 6 passive experts and 1 member of the city council

Group 3: 7 passive experts and 2 members of the city council

Group 4: 3 passive experts

Group 5: 2 passive experts and 1 member of the city council

Group 6: 3 members of the city council

Members of group 1, group 6, and (more or less) group 5 are the most independent in their opinions. Meanwhile members from group 4 and to lesser extent groups 2 and 3 are more influenced by other’s opinions.

The sum of influence of the active experts is equal to 2.873 (Teacher), 1.471 (doubtful expert) and 1.657 (Independent Expert). In this case we obtain the influence of the group of “teachers” which function as a team (with μ=1 and λ=0) have nearly the same effectiveness as the sum of the other participants.

5.       CONCLUSIONS

The method that was developed here can be applied to research any social network that meets the following conditions:

-       The network has an exchange of ideas among the participants and evaluation of those opinions by different members of discussion;

-          The network has set of topics for discussion.

The proposed method allows measuring a level of effectiveness of the educational mission of the forums through the comparison of influence of the teaching team members to other (independent) participants of the educational forum.

It was shown that the proposed method allows us to know who in a given group of people are leaders and who are followers through the calculation of μ and λ. With the results of the measurement of μ and λ, we can correct the soft educational strategy through the forum, which we consider to be an educational tool of humanitarian technologies.

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2. Makagonov P., Celia Bertha Reyes Espinosa (2008-b). Developing Website of Regional Cul­ture Center and Social Networks. International Workshop on Social Networks and the Applica­tion Tools. September 19-21, 2008. University of Central Europe and SoNet Research Center Skalica, Slovakia (European Union).
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