Abstract

۱٫ Introduction

۲٫ Related works

۳٫ Material and methods

۴٫ Behavioral properties of C-MSN

۵٫ Experimental results

۶٫ Conclusions

Declaration of Competing Interest

References

Abstract

     Social networks are electronically information sharing systems, due to this case, there are many studies on social networks. When studying social networks, text-based solution methods can be used; this type of study is outside the scope of this paper. Some studies have used mathematical models such as graphs, and graphs are mathematical models to represent many things, and social networks are one of them. However, graphs are static models whose structure cannot match the behaviors of social networks. To get rid of this case, Petri nets have been used in some recent studies , however, they have some deficiencies (obtained models are not complete and sound). Because of this case, we modeled social networks by using Petri nets. The resulting model is called Marked Social Network. The marked social network has two types such as Concurrent Marked Social Network and Parallel Marked Social Network. The obtained models were analyzed in case of behavioral and structural properties, and the major properties of the model were determined. All these properties are described in this study.

Introduction

     Social networks were developed after electronics information sharing systems coming out, and social networks are modeled by using graphs. Due to the interests of users and capabilities of social networks, this area is an important emerging area, so, there are many studies of social networks such as community detection, stance detection, privacy-preserving proximity detection, anomaly detection, irony/sarcasm detection, role mining, topic/event detection, and causality detection.

۱٫۱٫ Community detection

     Community detection is the problem to detecting groups in networks whose characteristics are similar and they are tightly-coupled [3]. In other words, a community can be also described as “a group of entities/that are in proximity of each other when compared to other entities of remaining networks” [۳]. The community detection can be handled by using clique detection in the graph which is a mathematical model of the related social network, or compact group discovery can be handled by using graphs [8], [11].

۱٫۲٫ Stance detection

     Stance detection is a social network issue that illustrates that an individual who gave an opinion about a certain target is neutral, against, or favor towards the target. In another word, stance detection can be regarded as opinion mining or sentiment analysis [13].

Conclusions

     The social networks are modeled by using graphs; however, graphs are static models and they cannot model the dynamic properties of social networks. Due to this case, we modeled social networks by using Petri nets. The obtained Petri net model was named Marked Social Networks. The Marked Social Networks have two types such as Concurrent Marked Social Network and Parallel Marked Social Network. The major properties of these networks were analyzed in this paper. An important point is that both models (C-MSN and P-MSN) are deadlock-free, so they can be used to model real-life applications. However, the P-MSN model is more suitable because of the waiting times in the C-MSN model.

     In this study, a general mathematical model for social networks is presented. This model can be customized for different social networks. In future studies, this model will be expanded and applied for different analyzes on various social network groups.