Mathematical Questions in Social Network Analysis

In last three lectures, the SNA which is the most useful and accurate tool to explain the pattern of interaction between actors has been introduced in detail by Prof. Rosanna. Through the SNA, abstract social relationship could be transformed into math model to measure and calculate which might be more convenient to study and make decisions for researchers in further. More specifically, there are numerous methods in SNA, from graph theory to socio matrix, from centrality to prestige, and all the way to ranking. However, in my opinion, there are some trifles need to be decomposed, although the lecture notes has involved almost of all aspects in SNA.

1.      Powers of a Matrix

From the lecture, I am confirmed that every classmate could write the zero-one matrix to express any social relationship. However, in terms of powers of a matrix, maybe we have something confused. Now, let us review the knowledge of linear algebra learnt before. To matrix X, if X_ij=p (X_ij is the element in the i^th , row j^th column), that implies the number of methods from n_i to n_j walking length n is p. Therefore, in social networking, the entries of the matrix X^p give the total number of walks of length p from node n_i to n_j and the value of X_ij in X^p gives the quantity of probability. Here, we might surprisingly find why there is relationship between A and B in matrix X, the value being 0 in X² , but in X³ they have relationship as well. Maybe we can draw a picture like this.

From the picture, length 1, A to B, length 2, we cannot find any ways, and length 3, there is a way A to C to D to B. Obviously, these properties would be same for both directed and nondirected graph.

2.      Group Degree Centralization

In terms of the calculation formula

Where, g is the number of actors.

C_D(n^*) means the largest degree of actor, C_D(n_i) implies the number of degree of actor n_i. So we could calculate the numerator easily. For the denominator, there might be something confused with the meaning of “max”. In fact, it could be understood as the max value of numerator in entire probable topology patterns including star, circle and line etc.. To estimate the denominator, we should let C_D(n^*) become largest and C_D(n_i) become smallest. Undoubtedly, maximum value of the denominator occurs when the network is in star shape, which equals to numerator in star shape. Therefore, we could deduce it is (g-1)(g-2) and C_D =1 in star shape definitively.

3.      PageRank

Before discussion of the PageRank, there is need to have a review of Rank prestige. To the topology

The sociomatrix X is

p = X’p, Which corresponds to the system of equations

On the other hand, the calculation of PageRank is still ambiguous after reading the content of Slide 25 in Week 9. What does the formula  mean? And how to use it?

We could analysis every element step by step first. To Actor A, the direction to it is just C, but the Actor C directing to other actors is just A as well. So

 To Actor B, the direction to B is just A, and A directing to B and C which make up of 1/2. Hence,

To Actor C, the direction to C is A and B, A directing to B and C which make up of 1/2, and B only direct to C. Therefore, 

Having a detailed understanding and recognition of these mathematical questions, there are no obstacles to analysis the social model and psychology. Actually, there are some other interesting parts of SNA not included in the article, and you might dig them personally. 

Social Behaviors on the Internet

To learn social behaviors on the Internet, we studied a case about social cloud computing last class. The main idea of the article is that each community could achieve resource sharing through cloud computing and cloud storage.

In terms of the definition of social cloud, my understanding is that a social cloud is a resource and service sharing framework utilizing relationships established between members of a social network. In addition to that, the second problem Prof. Rosanna proposed “what are the possible applications of a social cloud?” In my opinion, it might conclude social computation cloud, social storage cloud, social collaborative cloud, social cloud for public science and enterprise social cloud, which could be resolved easily for the unambiguous structure of the article. What we should admit is that there are several disadvantages and imprecision in the article, among these, the biggest drawback might be the privacy. As the former part said in the article, “Users are more likely to trust information from a “friend” if the digital relationship between the two is based on a real world relationship (friend, family, and colleague) rather than a purely online relationship (second life, online games, etc).” Therefore, we would public our private information and life status, but we cannot guarantee that all the online friends could know each other and like to share our stories. What’s more, some people just look like our “friends”, and we maybe have a chip on their shoulders. Nowadays, there is a status between cognizance and incognizance named “I have his Facebook”. It might be a kidding, but a common sight in our life. Hence, the problem of individual privacy in social networking has emerged and extends further. On the other hand, socially motivated resource sharing indeed provides us so much convenience in study, life and work. Thanks to wireless application, more and more people use Dropbox instead of USB flash disk. Then the issue has emerged, we could guarantee the truth of materials in USB flash disk in the reason that we could hold it everywhere and every time. However, the resources on social cloud are easily shared by everyone. Whether the materials have been cut or modified we might be not sure. As a result, we face the truth of them with a grain of salt.

During the period of class activity two, our group discussed deeply the former questions as well. As a consequence, we hold the same opinion about the definition of social cloud and possible applications, because these problems are so simple for us to find the answer in article fast. However, in term of drawbacks, participants in our group had numerous arguments, such as private issues, and offer resolutions, like setting the authority. Meanwhile, we also provide some questions about confused parts. A simple example would be like this, Sabrina said “I wonder why people will trust a real world friend more than a pure online relationship? I know it may true but who know the basis.” I am confirmed that it is the networking security bringing about fear for users. Belonging with more and more Internet fraud emerging, users feel less the trust on friends who know online, especially facing the personal privacy. When come to a stranger who meet right now online and want to know your phone number, you might hesitate, which means you do not trust in him completely. But the person would be your friend in real life, and you might not feel that hesitation. Besides that, this question can be explanted in epistemic cognition theory, which is so simple and do not be discussed here.

  

Thus it can be seen that there exist some differences between individual and group epistemic cognition. When I learnt the case, first of all, I scanned total content, understand and explain. Step by step, to acquire true, justify beliefs and to avoid false beliefs, I could promote cognition into metacognition and epistemic level. However, during this period, there is no any new knowledge to be come into being. On the contrary, in the process of group discussion, participants could exchange their ideas and build knowledge together in a social environment. In term of given questions, participants tried to find the answers, form the new knowledge system which help to collaborative knowledge construction. All participants set forth their ideas and negotiate a fit between personal ideas and ideas of others. Through a sustained improvement of ideas and understanding, participants create higher level concepts. For the limited time, participants were also encouraged to contribute new information to central resources, to reference and build on authoritative sources.

Personally, the way to approach to the problem individually and in group, respectively, is various as well. On one hand, individual behavior could not be immune by curiosity or anger over being criticized. On the other hand, in group works, total participants can interact continuously to improve the quality, coherence, and utility of ideas. At the same time, a good social environment that facilitates knowledge building should provide support for theory construction and refinement and for view ideas in the context of related but different ideas. Further, team members produce ideas of value to others and share responsibility for the overall advancement of knowledge in the community. In addition, participants can embed authoritative sources (e.g. news, videos), along with other information sources, as data for their own knowledge building and idea-improving processes.

To conclude, we cannot deny that community with more possibilities than individuals to improve and emerge new knowledge construction. Moreover, it is an indispensable part in the process of cognition.

Communication Networks and Network topologies

Communication Networks

The communication pattern describes the physical and logical arrangement of the participants in relation to each other within a network or during communication. However, they are not same. At the class, Prof. Rosanna introduced communication patterns in problem solving involving 5 people. The five-people communication network can be organized into: circle, concom, wheel, Y, and chain.

Concom--the most complex method is to create a mesh connecting all the participants with each other via separate communication lines. When it comes to network extensions, the flexibility is very low and it involves no leader in the group. However, in my opinion, there are any patterns without the higher participants’ satisfaction than concom.

When several two-point connections are used to create a physical ring, we speak of circle. It is similar as the concom but a little bit simpler. Also, there is no leader in the pattern.

A much clearer and simpler structure is the chain pattern. In this case, all participants communicate over the same line. Therefore, the transmission efficiency of messages is lower than others. Leader emerging and participants’ satisfactions is both moderate.

The Y pattern is in most respects similar to the chain pattern, except that the Y structure enables several participants to be connected in the same one. Hence, the leader emerging and participants’ satisfactions are similar as the chain pattern.

In the wheel pattern, all participants are connected to a core leader. Obviously, the leader emerging is highest in the 5 patterns. In both cases, failure of the center one causes the entire network communication to fail. As the surrounding participants cannot communicate each other, the participants’ satisfaction is the lowest in all at the same time.

Network topologies

Except for several patterns, we could need software to help us analysis the network topologies. For example, the Visio add-in, who’s created network maps can be documented and shared by exporting them as XML files or to Microsoft Visio 2007.

Add-in for Microsoft Visio 2007. This add-in helps you export the network maps or business views from OpManager to Visio. Refer to the help documentation for details.

It makes sense to group the devices that need special attention under one consolidated view even when they are spread across subnets. That’s exactly what OpManager’s custom maps or Business views section offers.

OpManager’s customnetwork map lets you group the devices based on the need. Further, one can add any background images, draw a live link between devices, export the custom maps to Microsoft Visio and even create a shortcut for a dependent business view in the parent business view.

Knowledge of networking topologies is core importance of computer networking design. Computer networks can  be developed using the knowledge about these topologies and decide to which topology design is best suited according to the requirement.

Metacognition - Thinking about thinking

Simply speaking, metacognition is thinking about thinking. More specifically, Taylor defines metacognition as “an appreciation of what one already knows, together with a correct apprehension of the learning task and what knowledge and skills it requires, combined with the agility to make correct inferences about how to apply one’s strategic knowledge to a particular situation, and to do so efficiently and reliably.”

Metacognition and Three Types of Knowledge

To increase their metacognitive abilities, students need to possess and be aware of three kinds of content knowledge: declarative, procedural, and conditional. This notion of three kinds of knowledge applies to learning strategies as well as course content. When they study, students need the declarative knowledge that all reading assignments are not alike; for example, which a history textbook chapter with factual information differs from a primary historical document, which is different from an article interpreting or analyzing that document. They need to know that stories and novels differ from arguments. Furthermore they need to know that there are different kinds of note taking strategies useful for annotating these different types of texts. And students need to know how to actually write different kinds of notes (procedural knowledge), and they need to know when to apply these kinds of notes when they study (conditional knowledge). Knowledge of study strategies is among the kinds of metacognitive knowledge, and it too requires awareness of all three kinds of knowledge.

Metacognition and Study Strategies

On the class, Prof. Rosanna had given some examples of metacognition applied in our social life. However, there is still a question left to be discussed. What other features you add on to a social website to facilitate user experience at a metacognitive level? Absolutely, we could find many examples, such as the tribes in DouBan Community, labels of blogs, and the rank of restaurants in OpenRice. We cannot deny that it is pretty convenience for our search.

Metacognition and Motivation

Metacognition affects motivation because it affects attribution and self-efficacy. When students get results on tests and grades on assignments, they perform a mental causal search to explain to themselves why the results happened. When they achieve good results, students tend to attribute the result to two internal factors: their own ability and effort. When they fail, they might attribute the cause to these same internal factors, in a self-protective rationalization, distance themselves from a sense of personal failure by blaming external causes. This tendency to attribute success to ability and effort promotes future success because it develops confidence in one’s ability to solve future unfamiliar and challenging tasks. The converse is also true.

To sum up, metacognition is an indispensable part when we know about the world. Understanding and applying the purpose and condition of knowledge is a kind of self-efficacy. It is helpful to develop our study when strengthening the training like this. Now, let us think about thinking!

Crowdsourcing-breaking up the whole into parts

What we have learnt from the introduction of Prof. Rosanna during the last two weeks helps us to set up a holistic overview of social media and social networking. In addition to that, there were a variety of examples of social tasks and media from China mainland or foreign countries shared by Prof. Rosanna and participants, which left an impressive comprehension on social networking.

Although most of youngsters have joined in social networking and refresh Facebook or Twitter every day, the social technology and knowledge which we get is limited because of the not long history of social networking. As one of them, I just focused on social websites and media before.  However, it is a narrow definition about social networking which also involve social tasks such as crowdsourcing. As almost of all students, I have never heard about it before, but we cannot deny we all encounter even use it when surfing the Internet. Simply speaking, crowdsourcing means posing a problem to a crowd of users that is impractical to solve through computation but is possible through human analysis. Then Prof. Rosanna gave us plenty of examples of crowdsourcing which maybe not leave an impressive comprehension because they are all foreign websites and never used before. However, as I know, there is some social networking similar to them in China mainland.

For example, the BurdaStyle is a website which could help you choose cloth and analysis which one is more fashionable. On the contrary, Melishuo and Mogujie are not strange for students from China mainland. Though the platform, there are large number of fashionistas sharing their thoughts, shopping experience and matching methods.

Another example will be like this, .Dopplr social site allows members to share their upcoming travel destinations, and BrightKite helps people discover each other based on geolocation through cellphones. Actually, Momo and Weixin also have similar functions, and are widely used in transportation. It is a common sight that taxi drivers select proper passengers around though geolocation measurement. It is convenient and efficient for both drivers and passengers.

However, there is still one kind of social networking which may not be popular as others and is not mentioned in the lecture. It is a platform for original singers. The original singers might have not enough money to publish recording and their works are easy to copy by other big record companies. This websites could protect their copyright; meanwhile, their works should be made into stocks. Listeners could buy what they like to support their idols and all of them could profit when the song is popular.

Generally speaking, crowdsourcing gives us some convenience and pleasure undoubtedly, but the problems which are exciting could be solved by crowdsourcing in daily life. Therefore, we would hold a considerate attitude to explore and discover social networking.