Rumor Spreading and Invasion Percolation

We study the models of rumor spreading and invasion bond percolation aimed at the revelation of possible connections between them. Rumor spreading model describes the dissemination of a rumor due to the periodical repetition of sequential phone calls, whereas the invasion bond percolation refers to the spread of liquid in the porous environment. During a round of the rumor spreading, each node performs a call only once, meanwhile transmitting all the information that it knows at the moment of the call to its neighbors. The rumor reaches the receiver node during one round if there is a chain of successive calls between the source of the rumor and that node. The sequence of calls is taken uniformly at random from the set of all possible sequences (permutations of nodes). We compare the propagation of the rumor spreading with the invasion bond percolation in order to put forth necessary improvements of the percolation rules to map one model onto another, and vice versa