In networks where massive sources make observations of same entities, we intend to seek the truth – the most trustworthy value of each entity from conflicting information claimed by multiple sources. Various methods are proposed for accurately inferring both source reliability and truths, yet relying heavily on centralized settings that incur tremendous overhead to source side. In this paper, we offer a decentralized design of truth discovery task that can fit favorably to the environments with limited resources. Considering that sources forming the connected network and making individual observations, we undertake the joint maximum likelihood estimation (MLE) of truth and source reliability. Our decentralization framework simply allows each source to maintain local information exchange at a time, and computes very basic functions of data observations. To this end, we facilitate the decentralization by simplifying the MLE problem into optimizing an objective function. Upon the proof of NP-hardness, two proposed decentralized algorithms (exact and approximation) are decentralized and randomized via a combination of algorithms from their centralized counterparts that ensure performance guarantee. The derived time complexity features explicit data/network dependent terms, which leads to further acceleration in truth finding. Remarkably, in two well connected networks like random geometric and preferential attachment graphs, the accelerated approximation method enjoys logarithmic time complexity while preserving comparable accuracy to the centralized counterparts. The effectiveness of the proposed decentralizations are further empirically confirmed.