It is a functional individual in social networks (including individuals, units, groups (whole)), which is represented by registered users, ID, etc. In a virtual network.

In the field of social network research, any social unit, social entity or functional individual can be regarded as a "node" or an actor.

In the figure: node set N={n 1, n2,,, n3}

2, line, relationship (relationship):

Data used to describe relationships, such as contact, contact, association, grouping and aggregation, link one agent with another, so it cannot be reduced to the attributes of a single agent. The arc as shown in the above picture.

Generally speaking, the points connected by a line are "adjacent" to each other, and adjacency is a graph theory expression of the fact that two actors represented by two points are directly related.

Generally, there are undirected lines, directed lines, multivalued lines and directed multivalued lines.

Graphs composed of lines include undirected graphs, directed graphs, directed multivalued graphs and undirected multivalued graphs.

3. Neighbors:

Those points that are adjacent to a particular point become the "neighborhood" of that point.

4. Degree:

The total number of points in the neighborhood becomes degrees. (Strictly speaking, it should be "connection degree"), and the connection degree of a point is a numerical laterality of its "neighborhood" scale.

Degree of a point (undirected graph). In the adjacency matrix, the degree of a point is expressed by the total number of non-zero values in the items of the row or column corresponding to the point. If it is binary, then the degree of a point is the sum of the row and column where the point is located.

In a directed graph, "degree" includes two different aspects, which express the direction of the line of social relations. They are called "penetration" respectively: the sum of points directly pointing to this point; And "out of degree": the total number of other points that the point directly points to. Therefore, on the matrix of a directed graph, the penetration of a point is the sum of the corresponding places in the column where the point is located. Range: On the sum of the lines where the point is located.

Sum of degrees of all points: the total degree of undirected graph can be checked by line (relationship), which is twice that of directed graph.

5, line (walk):

Each point can be directly connected by a line or indirectly connected by a series of lines. This series of lines in a graph is called "lines".

6. Path:

Every point and every line on a straight line is different, so this straight line is called "path", and the "length" of the "path" is measured by the number of straight lines that make up the path.

7. Distance:

An important concept refers to the length of the shortest path connecting two points (that is, shortcut). It is generally called the shortest path in graph theory. It should be distinguished from the concept of "route".

8. Direction

Mainly depends on the direction of the directed graph.

9, density (density)

Describe how closely the points in the diagram are related. "Complete graph" (called complete graph in graph theory) refers to a graph with all points adjacent to each other. Even in small networks, this kind of integrity is very rare. The concept of density attempts to summarize the total distribution of lines to measure the degree to which graphics have such integrity. The density depends on two other network structural parameters: the inclusion degree of the graph and the sum of the degrees of each point in the graph. Density refers to the overall cohesion level of a graph.

The concepts of "density" and "central potential" represent different aspects of the overall compactness of a graph.

Inclusion of graph: the total number of points contained in each related part of graph, which can also be expressed as the total number of points of graph minus the number of isolated points. The commonly used profile for comparing different graphs is: number of associated points/total points 15/20=75%.

Sum of degrees at each point:

Density calculation formula: the ratio of the number of lines actually owned to the number of lines possibly owned in the graph, and its expression is 2l/n(n- 1). ? The expression of directed graph is l/n(n- 1).

Density of multivalued graphs: it is necessary to estimate the multiplicity problem. Obviously, lines with high multiplicity and low specific gravity contribute more to the network density. A controversial measure.

Barnes (1974) compared two kinds of social network analysis:

10, Research on Egocentric Network

In social networks around specific reference points, density analysis focuses on the relationship density around certain specific actors. When calculating the density of individual center network, we usually don't consider the core members and the links directly related to the members, but only pay attention to the various links between these links.

1 1, Research on Social Center Network

Paying attention to the network correlation model as a whole is another contribution to social network analysis. From this point of view, density is no longer the density of individual network of local actors, but the density of the whole network. Density calculation has been mentioned above.

12 point centrality

The relative centrality of each point in the graph.

13, graph centrality is the concept of central potential.

14, global centrality (Freeman 1979, 1980)

Overall centrality refers to the strategic importance of this point in the whole network. According to the proximity between points, according to the distance between different points. You can calculate the sum of the shortest distances between a point in the chart and other points.

Undirected graph: The distance matrix between points in an undirected graph can be calculated by software, so a point with a lower "distance sum" is "close" to many other points. Proximity is inversely proportional to the sum of distances.

Directed graph: "inner closure" and "outer closure".

15, local center point

One point is associated with many points next to seven points. If a point has many directly related "neighbors", we say it is a local center point.

16, overall center point

If a point occupies a strategically important position in the overall structure of the network, we say it is the center of the whole.

17, local centrality (local centrality)

The relative importance of a local point to its neighboring points. The measurement is only based on the number of points directly connected to the point, ignoring the number of points indirectly connected. There are centripetal and outward centripetal in directed graphs. You can also define the distance as 1 or 2 for measurement. If it is defined as 4 (the distance between most points is 4), it is meaningless and has no information.

18, the relative measure of local centrality

The actual degree of a point is one of the most possible degrees, so pay attention to removing the point itself.

19, centralized Freeman (Freeman, 1979)

It refers not to the relative importance of points, but to the overall cohesion or wholeness of the whole graph. Few people try to define the structural central idea of a graph. The central potential describes the degree to which this cohesion can be organized around some points. Therefore, central potential and density are two important and complementary measures.

The difference between the centrality of the core point and the centrality of other points. Therefore, the concept is to compare the sum of the actual differences with the sum of the maximum possible differences.