Synthetic Generation of Social Network Data With Endorsements

In many simulation studies involving networks there is the need to rely on a sample network to perform the simulation experiments. In many cases, real network data is not available due to privacy concerns. In that case we can recourse to synthetic data sets with similar properties to the real data. In this paper we discuss the problem of generating synthetic data sets for a certain kind of online social network, for simulation purposes. Some popular online social networks, such as LinkedIn and ResearchGate, allow user endorsements for specific skills. For each particular skill, the endorsements give rise to a directed subgraph of the corresponding network, where the nodes correspond to network members or users, and the arcs represent endorsement relations. Modelling these endorsement digraphs can be done by formulating an optimization problem, which is amenable to different heuristics. Our construction method consists of two stages: The first one simulates the growth of the network, and the second one solves the aforementioned optimization problem to construct the endorsements.Comment: 5 figures, 2 algorithms, Journal of Simulation 201

Degree/diameter problem for mixed graphs

The Degree/diameter problem asks for the largest graphs given diameter and maximum degree. This problem has been extensively studied both for directed and undirected graphs, ando also for special classes of graphs. In this work we present the state of art of the degree/diameter problem for mixed graphs

Quasi-ordinarization transform of a numerical semigroup

We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction provides an alternative approach to the conjecture on the increasingness of the number of numerical semigroups for each given genus. We elaborate on the number of nodes at each tree depth in the forest and present a few new conjectures that can be developed in the future. We prove some properties of the quasi-ordinarization transform, its relations with the ordinarization transform, and we also present an alternative approach to the conjecture that the number of numerical semigroups of each given genus is increasing.Comment: arXiv admin note: text overlap with arXiv:1203.500