Agent-based model of information spread in social networks

Agent-based model of information spread in social networks D.V. Lande a,b, A.M. Hraivoronska a, B.O. Berezin a

a Institute for Information Recording NASU, Kiev, Ukraine b NTUU “Kyiv Polytechnic Institute”, Kiev, Ukraine

We propose evolution rules of the multiagent network and determine statistical patterns in life cycle of agents – information messages. The main discussed statistical pattern is connected with the number of likes and reposts for a message. This distribution corresponds to Weibull distribution according to modeling results. We examine proposed model using the data from Twitter, an online social networking service. Keywords: social network, modeling, Weibull distribution, agent-based system, information spread. Introduction The flows of information have a strong influence on opinion formation and other processes in the society. Today social networks play a fundamental role as a medium for the information spread. These facts motivate to explore mechanisms of creation of information flows and influence on them. Dealing with this requires focusing attention on modeling and finding laws or patterns in the spread of information [1]. In this article we present an agent-based model of information spread. The agent in this model is an information message [2]. A message published in social network may cause different types of public reaction. This model involves types of reaction such as positive or negative comments, respect or protest (we will call it like/dislike); message may be shared or copied (repost); also one message may have a link to another one (link). The evolution of the agent is controlled by mentioned above types of reaction. The main attribute of the agent is ―energy‖ (E); that is representation of current relevance of the message or a degree of interest to the topic of the message by people. Naturally, a positive reaction or appearance of link to the message cause increase of energy. In opposite way, energy decreases when the 2

message gets negative feedback. Anyway, energy tends to decrease because information eventually becomes outdated. The agent specification More precisely the rules of agent evolution are as follows. Each agent appears with the initial energy (E0) and dies when its energy becomes 0. The energy varies during the agent’s life cycle depending on the types of reaction. Let us list them all and their impact on the energy:  like: energy is incremented;  dislike: energy is decremented;  repost: energy is increased by 2;  reference: energy is incremented; In addition the energy is decremented at every time step (we consider the evolution in discrete time).
On the other hand, the more relevance of the message, the more likely people respond and express their opinion about information in this message. It is assumed the probability to get some response depends on current energy of agent. We introduce the probability of getting certain reaction for the agent with energy E as follows

     . 

We denote by initial parameters of the model, and by some monotone nondecreasing function from to [0, 1]. The simulation of information spread Earlier we introduced the evolution rules for the agent. The information flow consists of the set of such agents. We simulate the dynamics of the whole information flow as follows. At the initial time only one agent exists. New agents may appear in two ways. Firstly there is a probability of spontaneous generation ( ). It means that new agent may appear with probability at every time step. Such appearance 3

corresponds to the publishing new information by somebody. Secondly a copy of existing agent may be created (repost). Here we describe the life cycle of one agent in terms of variation of its energy. Let denote the value of energy at time t. Suppose is the random variable such that |

  |      (        

)

  |           

(

)
| (
) (

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Let us denote
| . Then we have

It follows that we can consider a change of energy as the random walk on { } with transition probabilities {

      {        }       

In other words the stochastic sequence is a Markov chain with transition probabilities . A state diagram for this Markov chain is shown on Figure 1, using a directed graph to picture the state transitions.

Figure 1. A state diagram for Markov chain. States represent energy of an agent

The random walk of energy is useful approach to analysis of properties of the model. 4

Model results Now let us consider the statistical distribution of likes and reposts for messages in the information flow. Note that we can find the probability to get n likes for one agent acco