Fixation probability on clique-based graphs
نویسندگان
چکیده
The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms graph changes from amplifier to suppressor as the fitness of the mutant increases. We demonstrate that the overall structure of a graph can be more important to determine the fixation probability than the degree or the heat heterogeneity. The dependence of the fixation probability on the position of the first mutant is discussed.
منابع مشابه
Constructing Ramsey graphs from small probability spaces
The problem of explicitly constructing Ramsey graphs, i.e graphs that do not have a large clique or independent set is considered. We provide an elementary construction of a graph with the property that there is no clique or independent set of t of nodes, while the graph size is t p log log t log log log t . The construction is based on taking the product of all graphs in a distribution that is...
متن کاملCohen-Macaulay $r$-partite graphs with minimal clique cover
In this paper, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$, then such a cover is unique.
متن کاملMutants and Residents with Different Connection Graphs in the Moran Process
The Moran process, as studied by Lieberman, Hauert and Nowak [10], is a stochastic process modeling the spread of genetic mutations in populations. In this process, agents of a two-type population (i.e. mutants and residents) are associated with the vertices of a graph. Initially, only one vertex chosen uniformly at random (u.a.r.) is a mutant, with fitness r > 0, while all other individuals ar...
متن کاملFinding Hidden Cliques of Size √(N/e) in Nearly Linear Time
Consider an Erdös-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset CN of the vertices that form a clique (a completely connected subgraph). We consider the problem of identifying the clique, given a realization of such a random graph. The best known algorithm provably finds the clique in linear time with high probability, provided |CN | ≥ ...
متن کاملFinding Hidden Cliques of Size \sqrt{N/e} in Nearly Linear Time
Consider an Erdös-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset CN of the vertices that form a clique (a completely connected subgraph). We consider the problem of identifying the clique, given a realization of such a random graph. The best known algorithm provably finds the clique in linear time with high probability, provided |CN | ≥ ...
متن کامل