Extending the definition of modularity to directed graphs with overlapping communities

Complex networks topologies present interesting and surprising properties, such as community structures, which can be exploited to optimize communication, to find new efficient and context-aware routing algorithms or simply to understand the dynamics and meaning of relationships among nodes. Complex networks are gaining more and more importance as a reference model and are a powerful interpretation tool for many different kinds of natural, biological and social networks, where directed relationships and contextual belonging of nodes to many different communities is a matter of fact. This paper starts from the definition of modularity function, given by M. Newman to evaluate the goodness of network community decompositions, and extends it to the more general case of directed graphs with overlapping community structures. Interesting properties of the proposed extension are discussed, a method for finding overlapping communities is proposed and results of its application to benchmark case-studies are reported. We also propose a new dataset which could be used as a reference benchmark for overlapping community structures identification.Comment: 22 pages, 11 figure

Detecting the overlapping and hierarchical community structure of complex networks

Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling to investigate different hierarchical levels of organization. Tests on real and artificial networks give excellent results.Comment: 20 pages, 8 figures. Final version published on New Journal of Physic

Improved community structure detection using a modified fine tuning strategy

The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this unduely constrains their results, leading to a bias in the size of the communities they find and limiting their effectivness. To solve this problem, we propose adding a step to the existing algorithms that does not increase the order of their computational complexity. We show that, if this step is combined with a commonly used method, the identified constraint and resulting bias are removed, and its ability to find the optimal partitioning is improved. The effectiveness of this combined algorithm is also demonstrated by using it on real-world example networks. For a number of these examples, it achieves the best results of any known algorithm.Comment: 6 pages, 3 figures, 1 tabl

Integrating organizational, social, and individual perspectives in Web 2.0-based workplace e-learning

From the issue entitled 'Special Issue: Emerging Social and Legal Aspect'E-learning is emerging as a popular approach of education in the workplace by virtue of its flexibility to access, just-in-time delivery, and cost-effectiveness. To improve social interaction and knowledge sharing in e-learning, Web 2.0 is increasingly utilized and integrated with e-learning applications. However, existing social learning systems fail to align learning with organizational goals and individual needs in a systemic way. The dominance of technology-oriented approaches makes elearning applications less goal-effective and poor in quality and design. To solve the problem, we address the requirement of integrating organizational, social, and individual perspectives in the development of Web 2.0 elearning systems. To fulfill the requirement, a key performance indicator (KPI)-oriented approach is presented in this study. By integrating a KPI model with Web 2.0 technologies, our approach is able to: 1) set up organizational goals and link the goals with expertise required for individuals; 2) build a knowledge network by linking learning resources to a set of competences to be developed and a group of people who learn and contribute to the knowledge network through knowledge creation, sharing, and peer evaluation; and 3) improve social networking and knowledge sharing by identifying each individual's work context, expertise, learning need, performance, and contribution. The mechanism of the approach is explored and elaborated with conceptual frameworks and implementation technologies. A prototype system for Web 2.0 e-learning has been developed to demonstrate the effectiveness of the approach. © Springer Science + Business Media, LLC 2009.postprin