Multi-scale Modularity in Complex Networks

We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales. It is first shown that methods based on modularity are not appropriate to uncover modules in empirical networks, mainly because modularity optimization has an intrinsic bias towards partitions having a characteristic number of modules which might not be compatible with the modular organization of the system. We argue for the use of more flexible quality functions incorporating a resolution parameter that allows us to reveal the natural scales of the system. Different types of multi-resolution quality functions are described and unified by looking at the partitioning problem from a dynamical viewpoint. Finally, significant values of the resolution parameter are selected by using complementary measures of robustness of the uncovered partitions. The methods are illustrated on a benchmark and an empirical network.Comment: 8 pages, 3 figure

Laplacian Dynamics and Multiscale Modular Structure in Networks

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multi-resolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multi-scale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms.Comment: New discussions on the selection of the most significant scales and the generalisation of stability to directed network

A Semi-automatic Method for Efficient Detection of Stories on Social Media

Twitter has become one of the main sources of news for many people. As real-world events and emergencies unfold, Twitter is abuzz with hundreds of thousands of stories about the events. Some of these stories are harmless, while others could potentially be life-saving or sources of malicious rumors. Thus, it is critically important to be able to efficiently track stories that spread on Twitter during these events. In this paper, we present a novel semi-automatic tool that enables users to efficiently identify and track stories about real-world events on Twitter. We ran a user study with 25 participants, demonstrating that compared to more conventional methods, our tool can increase the speed and the accuracy with which users can track stories about real-world events.Comment: ICWSM'16, May 17-20, Cologne, Germany. In Proceedings of the 10th International AAAI Conference on Weblogs and Social Media (ICWSM 2016). Cologne, German

Identifying communities by influence dynamics in social networks

Communities are not static; they evolve, split and merge, appear and disappear, i.e. they are product of dynamical processes that govern the evolution of the network. A good algorithm for community detection should not only quantify the topology of the network, but incorporate the dynamical processes that take place on the network. We present a novel algorithm for community detection that combines network structure with processes that support creation and/or evolution of communities. The algorithm does not embrace the universal approach but instead tries to focus on social networks and model dynamic social interactions that occur on those networks. It identifies leaders, and communities that form around those leaders. It naturally supports overlapping communities by associating each node with a membership vector that describes node's involvement in each community. This way, in addition to overlapping communities, we can identify nodes that are good followers to their leader, and also nodes with no clear community involvement that serve as a proxy between several communities and are equally as important. We run the algorithm for several real social networks which we believe represent a good fraction of the wide body of social networks and discuss the results including other possible applications.Comment: 10 pages, 6 figure