Looking at social networks from a mathematical perspective

Social networks are fun and confusing, and they want to find something that inspires mobile internet products from the social networks themselves, and their social networks are limited, and they have to turn to the experts ' books, which are notes on the "Social network analysis-Methods and Practices" book (Subway reading time).

Social network analysis (SNA) is the science and technology behind exploring relationships, looking at social networks from a mathematical perspective and exploring social networks in a graph-based way. Technically, a computable social network (Http://www.github.com/maksim2042/SNABook) is accomplished through the support of Python and related package files.

What is a relationship? In interpersonal relationships, in addition to friendship, influence, emotion, trust? The relationship can be two yuan, can also be assigned, can be symmetric, can also be asymmetric, the more common in reality is the Shuangfeng relationship or multimode relationship.

Based on the hypothesis of independence, some models can be set up by Poisson process or naive Bayes to make statistical analysis, and then the probability of some macroscopic results is obtained. But if we put aside the hypothesis of independence, we think that all relationships are potential dependencies, and that is where graph theory comes into play. Nodes represent the independent actors within the network, which represent the direct relationship of the actors, and thus describe social networks through TAMMOTU, dual-mode graphs, and multimode diagrams. Mathematically, the basic method of representing social networks is a matrix, but the adjacency matrix is too loose to store social networks in the form of edge lists.

The graph is used to describe the social network, the distance of the graph is a method to quantify the graph, and the shortest path and distance in information propagation can be obtained through the graph traversal.  We have learned the basics of software, depth-first and breadth-first search, in Networkx with ready-made algorithms dfs_edges and bfs_edges. For non-weighted graphs, distance means shortest path, and for weighted graphs, distance is the least cost path, and Euclidean distance is based on node similarity.

Who is the important person in the social network? Look at the number of edges of a node--the degree of centrality. The degree of centrality is the distribution of power law.

Who is the message propagator in the social network? Look at the reciprocal of the average distance of a node--close to the center, the larger the value the greater the viscosity.

Who is the transmission bottleneck? Look at the shortest distance of each pair of nodes, and then normalized processing-intermediary central, the greater the value of the more elite groups.

Who is the "Bishop of Grey"? It is equivalent to the center of the degree of recursion-eigenvector, which is the core of invisibility.

Google's PageRank algorithm can be said to be the center of the idea to play the most vividly, mobile products for the PageRank there is room for it?

For the elements that can be analyzed in a social network, the graph theory is described as a sub-graph and a group element. A sub-graph is a sub-network that is centered on a particular node, like "My Network" in LinkedIn, and it is a mistake to analyze a self-centered network with a network radius greater than 3.

Relationship has come:

1) Asymmetric connection, maintenance not more than two weeks

2) Symmetrical connection, more stable

3) The ternary group is the most stable over time, but there are three triples and structural holes which are forbidden to enter.

There are 16 possible scenarios for the ternary group, which were born in 1972, and I am about the same age. Triples form a sub-graph, and the largest complete sub-graph is the faction. The method of establishing a sub-graph is generally hierarchical clustering. People's ideas, attitudes and social relations are determined by the identity of the individual in the group, and the formation of the group stems from the attitude of the members.

In view of the different types of nodes, multi-mode networks are formed. From the two-mode network, you can create a subordinate network, as well as a homogeneous network. For multimode networks, matrix multiplication can draw a lot of valuable conclusions.

What an interesting thing to do if you can simulate a mobile social network? Initializes an empty network diagram and adds an object of n data types to it, then loops through the combination of each possible node, and when the probability equals the density parameter, adds a connection between the two nodes, which is called the Erdos-renyi algorithm, Is the simplest method of generating a random graph, and produces a distribution of a positive distribution, but in fact most social networks conform to a long tail degree distribution, which is the power law distribution.

Looking at social networks from a mathematical perspective