In this research, we exploit a novel approach for propagation processes on a network related to textual information by using topic modeling and pretopology theory. We first introduce the textual agent’s network in which each agent represents a node which contains specific properties, particularly the agent’s interest. Agent’s interest is illustrated through the topic’s probability distribution which is estimated based on textual information using topic modeling. Based on textual agent’s network, we proposed two information diffusion models. The first model, namely Textual-Homo-IC, is an expanded model of independent cascade model in which the probability of infection is formed on homophily that is measured based on agent’s interest similarity. In addition to expressing the Textual-Homo-IC model on the static network, we also reveal it on dynamic agent’s network where there is transformation of not only the structure but also the node’s properties during the spreading process. We conducted experiments on two collected datasets from NIPS and a social network platform, Twitter, and have attained satisfactory results. On the other hand, we continue to exploit the dissemination process on a multi-relational agent’s network by integrating the pseudo-closure function from pretopology theory to the cascade model. By using pseudo-closure or stochastic pseudo-closure functions to define the set of neighbors, we can capture more complex kind of neighbors of a set. In this study, we propose the second model, namely Textual-Homo-PCM, an expanded model of pretopological cascade model, a general model for information diffusion process that can take place in more complex networks such as multi-relational networks or stochastic graphs. In Textual-Homo-PCM, pretopology theory will be applied to determine the neighborhood set on multi-relational agent’s network through pseudo-closure functions. Besides, threshold rule based on homophily will be used for activation. Experiments are implemented for simulating Textual-Homo-PCM and we obtained expected results. The work in this paper is an extended version of our paper [T. K. T. Ho, Q. V. Bui and M. Bui, Homophily independent cascade diffusion model based on textual information, in Computational Collective Intelligence, eds. N. T. Nguyen, E. Pimenidis, Z. Khan and B. Trawiski, Lecture Notes in Computer Science, Vol. 11055 (Springer International Publishing, 2018), pp. 134–145] presented in ICCCI 2018 conference.