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This article was submitted to Social Physics, a section of the journal Frontiers in Physics

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Educational behavioral psychology refers to the fact that college students within campus networks have various psychological cognition toward novel information and behavior. This is hardly ever taken into account or theoretically examined in weighted network research. According to psychological traits and a student’s willingness to adopt fresh behaviors, we categorize students’ behaviors into the active and passive. On this basis, a threshold models is established for the behavior of active and passive students in weighted networks, and the influence behavioral psychology on information propagation is discussed. In order to qualitatively investigate the information propagation mechanism, a partition theory based on edge-weight and behavioral psychology is developed. Active students encourage the acceptance of new behaviors and the spread of information, according to theoretical study and simulation results. However, the phase transition intersected was more significant. When the percentage of enrolled pupils is high, a continuous phase transition is present in the growth pattern of the final adoption size. In contrast, as the proportion of active students declines, the increasing pattern alterss to discontinuous phase transition. In addition, weight distribution heterogeneity facilitates the dissemination of information and does not alter phase transition pattern. Finally, the theoretical analysis is in good agreement with the simulation results.

The campus socialization of college students has been paid more and more attention as a result of the gradual improvement of higher education. In campus socialization, students’ online information dissemination is becoming more and more crucial. The information propagation theory can be used to describe a variety of behaviors of college students, including social recommendation, online learning, online entertainment, among others.

For information propagation, researchers have investigated numerous potential influences on the information propagation mechanisms in depth studies for information propagation models, including node distribution structures [

Numerous research have shown that the spread of knowledge demonstrates social reinforcement or affirmation [

The distribution of information is also greatly impacted by the variability of individual closeness in genuine social networks. People are more likely to obtain information from their friends and family than from complete strangers. The influence of intimacy heterogeneity on information dissemination was confirmed by the researchers, who built the connective links between people as edges with diverse weight distribution [

Existing literature has suggested that populations are heterogeneous because different people have different attitudes toward the same action, for example [

Taking these factors into account, we investigated the effects of behavioral heterogeneity on weighted network information propagation. Only a small percentage of

We build a weighted social network model with

Additionally, edges with a weight distribution are used to indicate individual correlations. Then, in order to reflect the heterogeneity of edge, the distribution of edge weights is introduced. The edge-weight distribution is denoted by a function _{
ij
}. Indicate the likelihood that an S-state node will learn something from its A-state neighbor node by using the following notation:_{
ij
} = 1, it is demonstrated by _{
ω
} = _{
ij
}) increases monotonically as _{
ij
} increases.

Let _{
j
} = 0 (_{
j
} right arrow _{
j
} + 1, following the successful receipt of a message from the A-state neighbor I I across the relevant edge.

Additionally, two functions are suggested to illustrate the threshold for individual behavior in order to describe the effects of behavior heterogeneity on the dissemination of information, as shown in

The behavior adoption threshold function for conservatives is represented by

The following is a summary of the information propagation details in weighted networks. First, we chose a few of _{0} students at random to serve as the A-state node (seed) and all other nodes as the S-state. This information is transmitted from the A-state node to all neighbors through corresponding edge. The likelihood _{
ij
}) is matched by a weight of _{
ij
} when the S-State node _{
j
} → _{
j
} + 1 when the S-state node _{
p
} (_{
p
}), if _{
q
} (_{
q
}). The A-state node loses interest in the behavior after information transmission and changes to R-state with a probability of

The study of nonredundant information memory with behavioral heterogeneity on weighted networks is based on citations. On the basis of this, this paper puts forward a theory of information partition based on behavioral heterogeneity and analyzes the mechanism of personal information dissemination. Assume that the node in a cavity state [

The probability that the node will not get information from the following node is _{
w
}(

The likelihood that the S-state nodes _{
i
} will collectively get a

Think about the threshold functions for behavior adoption and behavioral heterogeneity. If the S-state node

The likelihood that the quantity of the aggregate information pieces by time

After receiving

Following that,

The likelihood that the S-state node

As a result, we can write the proportion of S-state nodes in a weighted network at time

We start by taking into account the _{
ω
}(_{
ω
}(_{
A,ω
}(_{
S,ω
}(_{
R,ω
}(

Then, we compute _{
S,ω
}(_{
j
} neighbors can obtain information from those _{
j
} − 1 in addition to the node

Think about the threshold functions for behavior adoption and behavioral heterogeneity. If the S-state node

After cumulatively accepting

Consequently, the likelihood that the node

With the corresponding weight margin _{
j
}, and

The evolutionary equation of _{
R,ω
}(_{
A,ω
}(_{
ω
}, the S-state node _{
ω
}(

On the other hand, the R-state node may transition from the A-state with a probability of _{
R,ω
}(

When the initial conditions _{
ω
}(0) = 1 and _{
R,ω
}(0) = 0 are combined with _{
R,ω
}(

Substituting

Substituting _{
ω
}(

Throughout the network, the density variation of each state can be expressed as

So, by combination and iteration

There are only S-state and R-state nodes in the network when

We conduct comprehensive numerical simulations and theoretical studies on weighted Scale-Free (SF) [^{4}; that is, there are at least 10^{4} dynamically independent persons in the network. The network’s average degree is

In our simulations, we employed the relative variance

We start by investigating how information spreads on a weighted ER network. The nodes of the ER network are subject to Poisson distribution, i.e.,

In a weighted ER network, _{
p
} = 1 and _{
q
} = 5, respectively.

Unit propagation probability’s impact on the final adaptive size of nodes in a weighted ER network with various percentages of active nodes, in beta. The phase transition is shown to be impacted by the heterogeneity of the weight distribution in (a1) (_{
ω
} = 2) and (b1) (_{
ω
} = 3). The relative variances and thresholds in subparagraphs _{0} = 0.01, _{
p
} = 1, and _{
q
} = 5.

The co-effect of _{
ω
} = 2) and 2) (_{
ω
} = 3). The initial fraction of seeds _{0} = 0.01. The adoption thresholds are _{
p
} = 1 and _{
q
} = 5. The crossover phenomena appears when

The final adoption size of a single weighted ER network is affected by the interaction of the unit propagation probability of beta and the active student part of p. There was no global behavior outbreak, discontinuous phase transition, or continuous phase transition in regions I, II, or III as described in subparagraphs _{
ω
} = 2 and 3, respectively). Other parameters are _{0} = 0.01, _{
p
} = 1, and _{
q
} = 5.

The degree index ^{−v
}, where _{
k
}
^{−v
}. The minimum and maximum degrees are, respectively, _{min} = 4 and _{max} ∼ 100.

_{0} = 0.01. The weight distribution exponent _{
ω
} = 2. The adoption criteria are _{
p
} = 1 and _{
q
} = 5, respectively. With the increase of beta,

Effect of _{0} = 0.01, _{
ω
} = 2, _{
p
} = 1, and _{
q
} = 5.

For a weighted SF network with _{0} = 0.01. Alpha _{
ω
} = 2, which is the exponent of weight heterogeneity. The adoption criteria are _{
p
} = 1 and _{
q
} = 5, respectively. Phase transitions occur as a result of the crossover phenomenon when beta increases. Even more exciting, when the degree distribution heterogeneity is highly heterogeneous, at

The combined impact of active student score and unit propagation probability on the final adoption size of weighted SF network users. The effects of (_{0} = 0.01, _{
ω
} = 2, _{
p
} = 1, and _{
q
} = 5.

This paper discusses the influence of behavioral psychology on the dissemination on campus sociality. We randomly select a small percentage of

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

JY and YC designed and performed the research and wrote the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.