In this chapter, the main discussion is that if the edges in the network are represented by ±, + means friends,-how will the network be distributed?Micro-individual strategies tend to show regularity on the macro level (Do you think Adam Smith, your late bread is not because of the gifts of others, but out of everyone's consideration of their own interests, the individual for their own interests is the social macro can be stable operation), in the social network is also such a distribution, The individual's consideration of the relationship with oneself makes the society divided into several parts in the macroscopic.
actions taken by individuals based on the consideration of their own relationship affect the social structure(Home is the smallest, the country is thousands-chan "country")
. Therefore, this chapter mainly considers the situation that two people are positive and negative relations.1. Structural balanceFirst of all, consider the overall social network is a complete picture of the situation.From the microscopic point of view, for three individuals, the equilibrium relationship is a triangle of three friends or a pair of friends and a common enemy of the triangle (in fact, I think three people are the enemy is quite balanced).The above definition of the microscopic structural balance is either a friend or a common enemy.For the whole, I look at not a relationship triangle, if it is a balanced triangle, then I can say that the whole is in a state of equilibrium.
2. Characteristics of structural Network balanceThere are two kinds of balance on the micro, so what is the macro?We can feel from the microscopic point of view, if three people are a good relationship, the corresponding whole is the world, we are the situation, we all are a harmonious state of relations (in the human infinite desire and limited resources of this contradiction between the contradictions if can achieve such an effect, I think it should be achieved Communism!! ）。Of course, the more practical situation is divided into camps. On the microscopic level, there are two people who unite as a camp to fight against the third camp more solidly (Wei). In society, then, this will lead to the division of society into two major camps. Each faction is a good brother, and the opposing camp is the enemy.
3. Application of structural BalanceStructural balance change trend: With the change of time, the study of network balance, society tends to balance, seems to be the use of the physical system to minimize the energy used in the model (cross-disciplinary results).International relations: not difficult to understand.Trust, suspicion, and online rankings: I think this jump is a big leap, from the layout of books, because in this online ranking, we can feel that some nodes seem to occupy a higher weight, and the ± number represents a hierarchical division. In other words, the ± has the effect of dividing the credibility. This is not simply a division, but a calculation of the weights of all nodes through trust and suspicion, so it can be applied to the rankings of users or products on the site.
4. A form of structural balanceIn addition to the two stable triangles above, let's add a seemingly unstable trilateral hostile relationship to the consideration, allowing the three sides to be hostile to each other.The result is that the society may be divided into many camps, the inner brotherhood, the camp between sword opposite.And the result of a three-party hostile weak balance is that the camp can be more, let's take a look at this interesting question for ourselves.We consider from a person's point of view, through the ± number of other people into friends or enemies. Unbalanced triangles are two +, one--that means my two friends if the enemy, this is not stable, so my friend must be friends, that is, + + + situation, for the enemy? If a certain requirement is +--, it means that there can be enemies, but no more enemies, because this relationship means that enemy enemies are friends and should be a dichotomy, divided into two sets. But when we allow----the enemy may also be our enemy, it is not necessarily a two-point map, there can be a lot of camp division, mutual hatred.This is the micro-scale of our relaxation of the balance limit on the macroscopic performance. Good fun ~
5. Extension of the definition of structural balance(The balance here is still a strong balance, not including---)1) before discussing the balance of the full graph, what is the structure balance in any network?2) for the balance, is it certain to achieve it? Can the balance be reached as large as possible, allowing a small portion of the imbalance?
1)Defining a non-complete graph is a balance chart: a sub-diagram of a fully balanced graph.In other words, it is a binary graph, but the edges can be less. Well, now the problem has been transformed into, given fixed-point sets and edge sets, how to determine the two-dimensional graph (combinatorial mathematical dafa good, why I feel and look for a set of things).
If the graph contains a circle with an odd number of negative relationship edges, it indicates that the graph is not balanced. (The general figure, the division of the two-part diagram, there is a circle if it is an odd number of edges, then it can not be divided into a two-part graph, because in the normal graph, the two endpoints of an edge determines two sets, in this task, the negative edge determines the two sets, both ends of the positive edge is the same set, so is to see the number of negative edges in the circle.
A callout chart is balanced when and only if it does not contain a loop with a technical negative closing edge. The proof method given in the book is that the adjacent friend node is abstracted into a super node, which makes the programming of the labeling diagram simple, and then according to a general figure to judge the two-part graph, the algorithm is the width-first search. (be classified as a known issue for resolution).2) Approximate Balance NetworkFor the original picture, the balance requirement is very high, can we relax this requirement?There are two ways to relax: To define other types of balance, which have been discussed before and increased--which gives us a weak balance. Or make the network not necessarily all the triangles are balanced, as long as a threshold is satisfied. Then it was the task of combinatorial mathematics.This is part of the story.
The positive relationship and negative relationship between network group and market in the 2015.4.1
