#### 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 [2], then it is transited under the local list [3] 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.

#### Re: Probability that all nodes of a p2p-network will be notified

Hello, Shmj, you wrote: S> Questions: S> 1. Whether there are any calculations minimum n which  unites all  in a network? S> 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.  only in case of connectivity everything, that is at n=N. All remaining only probabilities.

#### Re: Probability that all nodes of a p2p-network will be notified

Hello, Sharowarsheg, you wrote: S> Garantirovanno only in case of connectivity everything, that is at n=N. All remaining only probabilities. But the probability of origin of a subnet can be 1 of 10^1000000, for example. It is necessary to calculate. Experimentally, seemingly, even at n=2 for nodes from 1 million - the probability of origin of a subnet is very small.

#### Re: Probability that all nodes of a p2p-network will be notified

Hello, Shmj, you wrote: S>> Garantirovanno only in case of connectivity everything, that is at n=N. All remaining only probabilities. S> but the probability of origin of a subnet can be 1 of 10^1000000, for example. It is necessary to calculate. Experimentally, seemingly, even at n=2 for nodes from 1 million - the probability of origin of a subnet is very small. Initial conditions everyones are necessary, and events, in a case p2p networks, are not so casual. For example, on third of territory at present night, and the computers ungeared there - in itself already big aggregate - as them to consider? For practical applications I   from tens scenarios, would look at them, took n=10 and would calm down. For a theoretical substantiation  to write out the input data.

#### Re: Probability that all nodes of a p2p-network will be notified

Hello, Shmj, you wrote: S> Conditions: Probably,  it just yours. Still your model is similar on DHT something.