There is no relationship between the guests and their host. They all believe someone different has invited them to the island. Mr. Justice Wargrave thinks it is Constance Culmington, a woman he hasn't seen in eight years. Vera Claythorne thinks she was offered a job by a Nancy Owen, a woman who doesn't exist. Philip Lombard is hired by a third party, a Mr. Issac Morris, for a job he even Mr. Morris can't explain.Ms. Emily Brent is invited by someone whose handwriting she cannot read as a guest for a summer holiday. General MacArthur is invited by a Mr. U.N.Owen for a weekend with some of his "old cronies" to talk over old times. Dr. Armstrong thinks that he is going to see Mrs. Owens for health reasons. Mr. and Mrs. Rogers have been hired as help for the mansion on the island, and Mr. Blore has been hired as an investigator. Not one of them knows Mr. or Mrs. Owens, and, in fact, they do not exist. They figure out a little later that U.N. Owen actually stands for Unknown.
The thread that ties them together is that fact that they each have killed someone, either through neglect or planning. They do have a host, but he is one of them. I do not know if you have finished the book, and I don't want to spoil it for you. The real host delighted in killing, and he felt they were all getting what they deserved.