Leading companies worldwide are increasingly concerned about stakeholders’ needs. They include sustainability initiatives regarding the environment and the community in their business strategy and adopt a new way of communication with stakeholders, that is, the Integrated Report (IR). This document should include in just one document the information traditionally provided in the annual report, the sustainability report, and the corporate governance report. This article presents the IR phenomenon and pays special attention to the key concept of “connectivity,” according to the International Integrated Reporting Council (IIRC). However, Internet and digital technologies have provided new channels of communication and interaction through social media. Within the framework of the Legitimacy Theory, Reputation Risk Management, and Stakeholder Theory, this article argues that the new possibilities brought by social media can be most valuable for IR purposes as they are useful to increase transparency and stakeholder engagement. Having looked into 78 integrated reports for the year 2012 of the companies included in the IIRC pilot programme, our study posits that the level of IR connectivity (or its absence) can be due to the combination of three types of factors (information quality, corporate characteristics, and communication factors), using fuzzy‐set qualitative comparative analysis. Our findings confirm the equifinality tenet and the causal asymmetry principle. Very interestingly, in the sufficiency analysis, some factors always appear present (big size, long reports, and many channels of social media used) in the model for IR connectivity whereas in the model for non‐IR connectivity size and report length are always absent though the listing status is always present. This pioneering study is unique and valuable as it opens up a new line of research on IR and social media use, two of the latest trends in company reporting.