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In this paper, the model of the online real-time information transmission network, such as wechat, micro-blog, and QQ network, is proposed and built, based on the connection properties between users of the online real-time information transmission network, and combined with the local world evolving characteristics in complex network, then the statistical topological properties of the network is obtained by numerical simulation. Furthermore, we simulated the process of information transmission on the network, according to the actual characteristics of the online real-time information transmission. Statistics show that the degree distribution presents the characteristics of scale free network, presenting power law distribution, while the average path length, the average clustering coefficient and the average size of the network also has a power-law relationship, moreover, the model parameters has no effect on power-law exponent. The spread of information on the network represents obvious fluctuation scaling, reflecting the characteristics that information transmission fluctuates over time.

Network, Information Transmission, Real-Time Information, Fluctuation Scaling

With the rapid development of Internet application technology, a variety of social networking services (SNS) site is also expanding rapidly, such as Tencent, xiaonei net, happy net and so on. SNS has attracted tens of millions of Internet users through online chat, wechat, micro-blog and the sharing of the community platform. People form a so-called “acquaintance acquaintance” of large-scale online social networks, based on their personal social circles intertwined together, transfer and sharing of information through wechat, micro-blog, QQ chat and other channels. In recent years, with the development and wide application of Instant Messaging (IM) system, many scholars have done the research on the topology evolution mechanism of IM network. In 2000, Barabasi and Albert (BA) extended the BA network, and built a GBA (General BA) model, topological evolution driven by local events [

Online real-time information transmission network (ORITN), as a carrier of information dissemination, has its own structural characteristics. Take Tencent QQ network for instance, each QQ users usually add new QQ users into their circle of friends, according to their own interests and hobbies or real social relations, in their own limited social circles, so as to establish the connection relationship between users.

Meanwhile, the transmission of real-time information in the QQ network also has its own characteristics. For instance, whether a QQ user to forward a message or not is depended on the user’s interests or the role of trust between the different friends, so it is subjective, resulting in the transmission of real-time information and shows strong randomness. Moreover, the way of information's transmission in QQ network differs with the general online network [

In this paper, take QQ network for instance, we proposed and built the model of the online real-time information transmission network, namely ORITN, based on the connection properties between users of network, and combined with the evolving characteristics in social network [

Take QQ network for instance, each QQ user represents a unique node, the friends relationship between users represents the undirected edges, an undirected graph,

The connection between nodes in ORITN network, to a great extent, is a reflection of real interpersonal relationship. In reality, each person’s range of social activities is limited, showing the characteristics of local-world. Take QQ network for instance, QQ user i’s local network is equivalent to its social circle, just as “birds of a feather flock together”. On one hand, among its limited social circle, user i tend to add the active user j, thus the QQ network has the characteristics of local-world network [_{j}, namely node j’s degree. On the other hand, in the QQ network, when a new user joins the network and establish a connection with the old user, in addition to considering the activity level of each old node within the scope of the local-world, but also consider its cohesion in the whole network. The greater the cohesion of the old node is, the greater the probability of a new node is connected to it. In the ORITN network model, we introduce node-weighted to each node j, and use it to reflect the size of node’s cohesion, wherein, the node-weighted is denoted as

in which

Based on the analysis above, when node i add new contacts, we make the following assumptions about ORITN network model:

First, randomly select a certain number of nodes from the whole ORITN network to form a local network, wherein the number of the nodes is denoted by M, and the local network is denoted by

in which k_{j} means node j’s degree in the local network

Based on the model assumptions above, the algorithm of ORITN model’s topology evolution is as follows:

1) Growth mechanism: Initially, the initial network has

2) Local priority connection mechanism: Randomly select M nodes from the whole network to form a local network, which is denoted by

in which k_{j} means node j’s degree in the local network

After a t step evolution, an ORITN network is produced, in which the total number of nodes is

In this section, we use Matlab software to simulate the above-mentioned ORITN evolution model and analyze the statistical properties of the network topology.

First, apply the above evolutionary algorithm to generate an ORITN network model and set various parameters for numerical simulation. Then investigate its variation law of the degree distribution, the average clustering coefficient C and the average path length L of QQ network.

In this paper, simulation parameters are set as follows: initial nodes number

As is shown in

follows a power-law distribution,

Given

As is shown in

Given

As is shown in

In this section, the statistical properties of the real-time information’s transmission on ORITN are further analyzed. Firstly, we propose the rule of information transmission according to its transmission characteristics, and simulate the process of real-time information’s transmission on ORITN. Then statistics out the average times about the real-time information that nodes received through the transmission process, and take the average times as a time series. Afterwards, statistics out the standard deviation and average value of the time series, and find

the function relation between them. Then further analyze whether the spread of information on the network represents the characteristics of fluctuation scaling.

In reality, whether a user of ORITN transmits a real-time information is subjective, so it has a certain of randomness to transmit the real-time information on ORITN. Meanwhile, the information transmission is discontinuous, since the creation of real-time information is periodical and sudden. So in the process of information transmission, there may be a suspension, and then spreading it again. Based on the analysis above, we put forward the transmission rules as follow:

Step 1: Select a node i randomly from the network as a starting point for transmitting information, and create a new real-time information_{i}. Then each neighbor node j, who receive the information

Step 2: Start the transmission at a new time step. Among all the nodes that has received the information

It’s obvious that the random variable

Then

Application of Matlab software, we conducted simulation experiments of real-time information transmission on the ORITN network of N = 5010. The total time step for each experiment is T = 1000. The average results of 50 times repeated simulation are shown in

As is shown in

As is shown in

In this paper, take QQ network for instance, by analyzing the relationship between network users and information

transmission characteristics, we proposed and built the model of the online real-time information transmission network, namely ORITN. Through the simulation to model algorithm, we found some important properties of ORITN from the statistical data. For instance, the degree distribution of the network follows power-law distribution, and

The power exponent has nothing to do with the parameters of the network. Meanwhile, by simulating real-time information transmission process, the statistical analysis of time series of

This work was jointly supported by the National Social Science Fund (No.13BTJ009), the National Natural Science Foundation (No.61164020), and the Guangxi Key Laboratory of Spatial Information and Geomatics (No.1207115-27).