Diffusion on the Peer-to-Peer Network

In a peer-to-peer complex environment, information is permanently diffused. Such an environment can be modeled as graph, where there are flows of information. The interest such modeling that (1) one describe the exchanges through time from initial state network, (2) description used fit real-world case and to perform further forecasts, (3) it trace time. this paper, we review methodology for describing diffusion processes on network in context exchange crypto (Bitcoin) network. Necessary definitions posed, equation derived by considering two different types Laplacian operators. Equilibrium conditions discussed, analytical solutions derived, particularly directed which constitutes main innovation paper. Further innovations follow inclusion boundary conditions, well implementation delay equation, followed discussion when doing approximations useful implementation. Numerous numerical simulations additionally illustrate theory developed all along Specifically, validated, simple examples, analytic solutions, implemented them more sophisticated graphs, e.g., ring important networks. As conclusion article, fitting purposes order gain its diffusivity, scientific community aware of.