Reductionism and holism in complex network analysis method of "Original algorithm class"

0) Overview

Shortly before listening to an accomplished old gentleman, he told a lecture about simulation, which involved reductionism and holism. Therefore, through the wisdom of the gentleman, said to carry out the entire complex network analysis process (including the construction of complex networks, the same below) reductionism and holism.

This paper first expounds the definition of reductionism, holism and complex networks, then describes the relationship between complex network analysis and reductionism and holism, then puts forward some ideas for the improvement of some algorithms of complex networks and puts forward the concept of value path, and finally makes a further elaboration by using the algorithm of node strength and medium number of complex network as an improved example.

Because the author experience is limited, the example part does not have the picture and the detailed calculation process, therefore this article understanding may be slightly abstract, the interested friend may carry on the further communication with the author.

1) reductionism and holism complement each other

Holism is the universal connection between things, and reductionism is the inverse of the whole theory, that is, things can be split into parts (elements) to understand. At first glance, the thought of Holism and reductionism is somewhat contradictory, in fact they are complementary and indispensable. For complex networks, the process of splitting according to the function of Things (holism) based on reductionism is the process of complex network construction, which is based on the whole function of elements (nodes) and their relationships (the knowledge contained in reductionism) constitutes the process of complex network analysis.

2) reductionism and holism in complex networks

Qian Xuesen's definition of complex network is: The network with self-organization, self-similarity, attractor, Small world, partial or full nature without scale is called complex network. For the moment, regardless of the definition of the specific meaning of the various properties, we can simply and intuitively understand the network as a node and the relationship between the composition. As shown in.

2.1) complex networks and reductionism

When you decide to analyze things with complex network algorithms, you are using reductionism, which is also the process of network construction. A complex network is constructed by breaking things up into elements and their relationships based on the action of things.

Things have different effects, so the purpose of the analysis will be different. The different functions of things are reflected by different elements and by different relations, so the same thing, the purpose of analysis is different, the complex network can be different according to reductionism.

In addition, the process of restoration can be more than once, that is, things can be described by a layered network.

2.2) complex networks and holism

When the things are restored to the network, the relationship between the elements and the features becomes an independent objective existence. But if you want to use this network to describe the original things, you have to have all the objective (including nodes and relationships) as a whole to analyze. Some commonly used index algorithms in complex network analysis (such as degrees, interfaces, tightness, etc.) are based on this idea. This is also the overall theory in complex network analysis.

3) Some improvements in complex network algorithms

This article does not introduce improvements to the algorithms that are used in all complex network analysis. But this article will introduce the idea of algorithm improvement and take the intensity and the number as an example to further expound the improvement idea.

The network which is based on the function of things and reductionism is composed of knowledge, so the complex network is no longer a simple mathematical model, so the analysis results such as intensity and the number of interfaces based on the mathematical model are unreliable, which is similar to the grey correlation degree, principal component analysis, Algorithms such as factor analysis (I'll write a separate article in the future to prove that all of these methods are "ridiculous", as well as the links between complex network algorithms and such algorithms and how to improve them).

One way the mathematical model landed is to let it go into "life", so the improvement of mathematical model of complex network is to let it enter into the function of things, and to extract the knowledge contained in the network based on reductionism. The following is an example of the nodal strength and the number of interfaces (the same number of nodes and the number of edges).

improvement of 3.1-node strength algorithm

The strength of a node (feature), defined as the number of bars adjacent to the node. However, depending on the purpose of the analysis, not all sides (relationships) should be included in the calculation of strength, for example, in the network describing the football match, the player is defined as a node, the edge is defined as a passing or scoring between the players, and according to the strength of the player's goal, the player should not be included in the strength calculation.

The improvement of the 3.2-Medium number algorithm

The interface of a node (the number of edges and nodes) is defined as the ratio of the shortest path strip in the network graph to the total shortest path number.

The shortest path is mathematical and has no business (function) meaning, so its improved method is to operate the shortest path. In the network of football matches described in 3.1, the shortest path to the calculation of the number of points should be replaced with a path that contains at least the edge of the goal, which we can define as the value path, according to the node-number description of the player's contribution to the goal.

4) Summary

The process of construction and analysis of complex networks contains reductionism and holism. If the construction of complex network should be based on the function of things and the thought of reductionism, the function of things is extracted based on the theory of reductionism, and the function is applied to the computational algorithm in the complex network analysis which contains the thought of holism. You can replace the shortest path with a value path when calculating the number of interfaces.

The network which contains the theory of reductionism and holism is no longer the traditional mathematical network, and the diversity of the function of things determines the choice and complexity of different network algorithms in the actual analysis. It can be said that in addition to the understanding of algorithms in network analysis, the understanding and application of reductionism and holism in the construction and analysis of complex networks directly determine the reliability of the analysis results and the quality of the whole analysis process.

Clarification: This dish is full of "dabbler", seen and heard are extremely limited, easy to piantingpianxin, partial reading wrong, really scared. Write things also pick the simplest and easiest to write, if there is a wrong place to welcome criticism.

Another sweep code can pay attention to the public number of the dish.

Reductionism and holism in complex network analysis method of "Original algorithm class"