Barabasilab-networkscience Learning Note 3-random network model

The first contact with complexity science is in a book called Think Complexity, Dr. Allen speaks very well of data structure and complexity science, Barabasi is a well-known complex network scientist, Barabasilab is a laboratory he dominates, Here the note is about the course introduced in the slider notes, of course, other people's course is not a public class, so from the PPT can only see the backbone of things, to add, slider related books here can be found

To tell the truth this section of the slider I did not look very clear formula, poor math skills, if you can have a better explanation welcome message

The Random Networks (Erdös-rényi Model (1960)) was proposed by Pál Erdös and Alfréd Rényi, what is this thing? Look at the following wiki introduction:

Since the 1960s, the research on complex networks has been focused on random networks. Stochastic networks, also called random graphs, refer to complex networks produced by random processes. The most typical random network is the ER model presented by Paul Erdes and Alfred Reni. The ER model is based on a "natural" construction method: Assume that there is a node, and assume that the likelihood of each pair of nodes being connected is constant. The network that constructs this is the ER model network. Scientists initially used this model to explain real-life networks ^{[1]: 7-9.}

I think you probably know this network model, the link between nodes is completely random, slider in the end said that this model in reality is completely non-existent, we understand that this model is only to compare, to see in the absence of external factors (random case) This model has what characteristics, This allows us to better study other models.

When it comes to model characteristics, it is necessary to understand the characteristics of the incoming network, so that in the future to learn a better network model when a good comparison

The previous lesson mentioned three important features of the network model:

1. Degree Distribution:p (k)
2. Path Length: <d>
3. Clustering Coefficient:c

Do you remember? So this lesson is about the three features of the random network model to one by one analysis

In a closer look, the mathematical derivation of this is a method of applying stochastic processes, and network science (or science) is built on random processes (mathematics), which also shows the importance of learning them.

First of all, it's a two-item distribution, which compares this to a real-world network (some people collect Internet data to build networks, protein-structured networks, or Facebook networks). In reality, the distribution of power functions is often distributed (because of the convenience of data collection in our big Data age to verify that some models are correct, all models are based on reality, and the first step from reality is often data, the big data age, more focused on the level of data to go, Machine learning also extracts intelligence directly from the data, which suddenly reminds me of Newton's Law of motion and Kepler's Law of motion.

Random networks in order to have some evolution, and try to explain some of the phenomena of phase transition in physics (such as water to ICE), critical research is usually a typical nonlinear system, the so-called complex system, which is why the beginning says that the network is the heart of complex systems.

That dot distribution does not, path length? This seems to be a bit like the reality, the conclusion of the study in reality is called the Six degree theory, or the Small world.

and the clustering coefficient of random networks, which is very different from the actual network.

There are two important sliders in the slider to share with you:

All right, I'm going to get out of the lab, uncle, to see if I'm going, he's gone.

Barabasilab-networkscience Learning Note 3-random network model