Topic: Probability that all nodes of a p2p-network will be notified
Conditions: 1. There is a p2p-network, all nodes are equal. Well, type everyone yours. 2. There is an initial list of the nodes (IP address), which developers sew in the program. The part from them can be not accessible at the moment of program start (but were accessible at the moment of program writing). 3. Each node stores the local list of nodes to which broadcasts the information. Them n pieces. We name these nodes neighbors. 4. The node selects the neighbors in a random way: at first casual n working from the list , then it is transited under the local list  each of these nodes recursively. 5. Nodes accept the information from any interested person (not only from neighbors), write down in the basis. And accepting new - broadcast to all neighbors. All nodes are independent, fairly broadcast the information to the friend-friend. I.e. if one node transferred something to the neighbors (to nodes which holds in the local list), neighbors undertake to transfer already to the neighbors etc. Questions such: 1. What value n (neighbors) at which it is guaranteed all nodes will are connected with each other? That it did not turn out that you selected a certain casual node from the list, checked up its local list of nodes and casually it appeared that all these nodes are not connected to the main network, i.e. as though a subnet formed, broadcast to the friend-friend and the big network do not broadcast. The experimental method created some millions (naturally emulated, not the presents) and connected them in a random way. It appeared that presence casually selected 2 neighbors always connect a network in a single whole and for all time of experiments was a case that translation of one changed a state of all network. I hope, not too explained. Questions: 1. Whether there are any calculations minimum n which unites all in a network? 2. The same question provided that 50 % of nodes are and do not broadcast the information to the neighbors. I.e. You transferred to them and they with this do not do anything.