# Mutual Influence of Users Credibility and News Spreading in Online Social Networks
## 1 Introduction  
Online Social Networks (OSNs) have recently increased the ability of individuals to find information in real time, gathering news about disparate topics both in traditional situations as well as in extreme circumstances as risk and/or crisis scenarios. In these cases, where modern communication technologies could be temporarily unavailable or reports from the news outlet correspondents delay, information coming from eyewitnesses who report events shortly after they happened through posts in OSNs becomes a significant alternative. This phenomenon, called gatewatching [1], is a form of news reporting and commenting that does not operate from an authoritative position, rather it works by exploiting the collective intelligence and knowledge of dedicated communities to filter the news flow and to highlight and debate topics pertaining to those communities. Frequently, even traditional major press agencies collect information from these sources prior to breaking news and providing information, for example, they allowed to recognize in real time the outbreaks of infectious diseases [2] as in the case of Covid-19 [3], or to early detect the spread of seasonal influenza in order to organize containment measures [4; 5; 6]. OSNs were also used in the recent past to detect information about natural disasters, both to assist in managing rescue as well as in promptly warning affected populations to help as many people as possibile [7; 8; 9; 10; 11]. Beyond these extraordinary scenarios, the increasing amount of information available through these communities and related platforms often pushes people to prefer them instead of traditional channels to stay informed, therefore the responsibility for judgingthe content and accuracy of information moves from editors and journalists to online information users [12]. The main problem is that the information provided in OSNs often lacks professional gatekeepers to check content, i.e., people devoted to assess the veracity and relevance of news in order to choose which ones are worth to be publicly spread. If this can be interpreted as a natural consequence of the growth of user-generated content [13], a potential side-effect is the increase of fake news, because single users are usually less reliable than authoritative official sources in providing information [14]. Since news lacks the traditional markers used to determine source credibility, consumers become more responsible for making decisions about the credibility of information online and this results in a shifting towards the trustworthiness about information providers, that cannot be overlooked anymore and can effectively help in discriminating real from fake news. (Note that in this paper we will use the term trust and credibility interchangeably.) Trust in OSNs is actually influenced by several factors [15; 16]:  
* the propensity to trust, affected by each individual's psychology and independent of other OSN users;
* the set of mutual past interactions between users;
* the opinion each user has about the veracity of others' posts; note that acquaintance between two individuals does not imply mutual trust, rather it can be dynamically inferred by observing the users social behaviors over time. In this paper, taking inspiration from [16], we evaluate how trustworthiness among OSNs users influences the news spreading and viceversa, in particular we first model the news spreading as an epidemic process that can be effectively studied with Susceptible-Infected-Recovered (SIR) approach [17; 18]. We added to the original formulation provided by [PERSON] [19], the contribution of OSNs user credibility (a.k.a. trust [20; 21]) to reproduce their real behavior, being people willingness in spreading news actually affected by their trustworthiness of information sources. We model the credibility of users with an additional weighted directed layer, namely the Credibility network, that complements the acquaintances network naturally present in OSNs.