there is a union of the two adjacencies set as shown in a measure of rightness. Since the ordering procedure Figure 5 and represented by positions to each node, the mean positions of that are already related to the central node, is the function value. The smaller this value is the better is the B3u= de weighting set being considered This index measures the cohesion between the " bisset weigth formed by the friends of i and friends of j. A good index 2 weigth weigth does not necessarily means a good index 3. In other words, a rson that belongs to my work environment, for example Parent110011100101000100111 does not necessarily have friends that is relate in any way friends In gener ral. So the second index betwe een me Parent210001100101110101010101 and a work friend can appear strong, but as their friend have no relationship with my friends, the third index will 101011000010101001001101 Children100001110010101001001101 C. Index Weight Calibration Using Genetic Algorithm The calibration step is the procedure that combines the 101011001011100001001101 multiple indexes, three in this case, into a single value. This value is used to obtain the final set of ordered results for the ecommendation mechanism. A simple procedure to obtain this value is to use a weighted average among the indexes. Fig. 6. Generation of several children strings obtained from two parents However, an Genetic Algorithm is used to optimize The crossover of the gene from the parents is randomly obtained dexes value so to obtain the best ordered result A self-adjustment mechanism should be more practic he purpose of the recommendation system. This mechanism should choose different indexes for different users. Since each user has his particular relationships pattern, preserving these patterns is the best choice for a recommendation mechanism for it to be more effective. A self-adjustment mechanism needs to be able to calibrate the weights in relation to the optimization function, which is given by n A(n, w)=I(ne,n).W,+I2 (nc,n).w2+I3(nc, n).w The calibration step can be defined as an optimization problem. In this case, we use a genetic algorithm to solve this optimization. The fitness function is defined in the above equation, where Ii, represents the index and wi the weights that we wish to optimize order to find the solution. Each individual of the population is composed of 3 Fig.5.The rounded vertex, minus the black and white vertex, composes the weight of each index. The evolutionary process is done with analyzed set on third index. [10]. Each new generation replaces the worst individuals by The weight calibration of each single index must be children of the best individuals. The crossover is done in a adjusted to obtain an optimized result. In this case, single random cutoff point as shown in Figure 6. Each pair optimization means classifying the most important users in of parents can produce many children as long as there are no the beginning of the list. The importance of a user on the duplicates in generation. After a generation of children every social network depends in the context. This context can bit of the new string is passed through the process of change depending on the user who is searching for the mutation. A high mutation rate was applied, 4%o for each bit, recommendation. Therefore, the optimization function must enough to prevent the loss of diversity in the population, consider the existing relationship structure of the user which could lead to premature convergence. The initial To create the optimization function for the weights, a population contained 200 individuals randomly generated modification has been proposed in the filtering step The The algorithm until no improvement occurs in the filtering step needs also to include the nodes directly related fitness of the best individual for 4 consecutive generation to the central node of the global recommendation process The fitness function used the classification of these nodes asthere is a union of the two adjacencies set as shown in Figure 5 and represented by:  =  ∪ This index measures the cohesion between the “big” set formed by the friends of i and friends of j. A good index 2 does not necessarily means a good index 3. In other words, a person that belongs to my work environment, for example, does not necessarily have friends that is relate in any way with my friends in general. So the second index between me and a work friend can appear strong, but as their friends have no relationship with my friends, the third index will appear weak. C. Index Weight Calibration Using Genetic Algorithm The calibration step is the procedure that combines the multiple indexes, three in this case, into a single value. This value is used to obtain the final set of ordered results for the recommendation mechanism. A simple procedure to obtain this value is to use a weighted average among the indexes. However, an Genetic Algorithm is used to optimize the indexes value so to obtain the best ordered results. Fig. 5. The rounded vertex, minus the black and white vertex, composes the analyzed set on third index. The weight calibration of each single index must be adjusted to obtain an optimized result. In this case, optimization means classifying the most important users in the beginning of the list. The importance of a user on the social network depends in the context. This context can change depending on the user who is searching for the recommendation. Therefore, the optimization function must consider the existing relationship structure of the user. To create the optimization function for the weights, a modification has been proposed in the filtering step. The filtering step needs also to include the nodes directly related to the central node of the global recommendation process. The fitness function used the classification of these nodes as a measure of rightness. Since the ordering procedure defines positions to each node, the mean positions of these nodes that are already related to the central node, is the fitness function value. The smaller this value is the better is the weighting set being considered. Fig. 6. Generation of several children strings obtained from two parents. The crossover of the gene from the parents is randomly obtained. A self-adjustment mechanism should be more practical for the purpose of the recommendation system. This mechanism should choose different indexes for different users. Since each user has his particular relationships pattern, preserving these patterns is the best choice for a recommendation mechanism for it to be more effective. A self-adjustment mechanism needs to be able to calibrate the weights in relation to the optimization function, which is given by: (!, #) =  (!$ , !). # +  (!$ , !). # +  (!$ , !). # The calibration step can be defined as an optimization problem. In this case, we use a genetic algorithm to solve this optimization. The fitness function is defined in the above equation, where  , represents the index and # the weights that we wish to optimize in order to find the best solution. Each individual of the population is composed of 3 bytes. Each byte, ranging from 0 to 255 represents the weight of each index. The evolutionary process is done with a binary genetic algorithm with uniform state replacement [10]. Each new generation replaces the worst individuals by children of the best individuals. The crossover is done in a single random cutoff point as shown in Figure 6. Each pair of parents can produce many children as long as there are no duplicates in generation. After a generation of children every bit of the new string is passed through the process of mutation. A high mutation rate was applied, 4% for each bit, enough to prevent the loss of diversity in the population, which could lead to premature convergence. The initial population contained 200 individuals randomly generated. The algorithm runs until no improvement occurs in the fitness of the best individual for 4 consecutive generations. 236