Abstract: This paper objects to extend Jon Kleinberg-s research. He introduced the structure of small-world in a grid and shows with a greedy algorithm using only local information able to find route between source and target in delivery time O(log2n). His fundamental model for distributed system uses a two-dimensional grid with longrange random links added between any two node u and v with a probability proportional to distance d(u,v)-2. We propose with an additional information of the long link nearby, we can find the shorter path. We apply the ant colony system as a messenger distributed their pheromone, the long-link details, in surrounding area. The subsequence forwarding decision has more option to move to, select among local neighbors or send to node has long link closer to its target. Our experiment results sustain our approach, the average routing time by Color Pheromone faster than greedy method.
Abstract: We study how the outcome of evolutionary dynamics on
graphs depends on a randomness on the graph structure. We gradually
change the underlying graph from completely regular (e.g. a square lattice) to completely random. We find that the fixation probability increases as the randomness increases; nevertheless, the increase is
not significant and thus the fixation probability could be estimated by the known formulas for underlying regular graphs.
Abstract: In this paper we introduce the notion of protein interaction
network. This is a graph whose vertices are the protein-s
amino acids and whose edges are the interactions between them.
Using a graph theory approach, we identify a number of properties of
these networks. We compare them to the general small-world network
model and we analyze their hierarchical structure.