Hierarchical community structure in complex (social) networks

The investigation of community structure in networks is a task of great importance in many disciplines, namely physics, sociology, biology and computer science where systems are often represented as graphs. One of the challenges is to find local communities from a local viewpoint in a graph without global information in order to reproduce the subjective hierarchical vision for each vertex. In this paper we present the improvement of an information dynamics algorithm in which the label propagation of nodes is based on the Markovian flow of information in the network under cognitive-inspired constraints \cite{Massaro2012}. In this framework we have introduced two more complex heuristics that allow the algorithm to detect the multi-resolution hierarchical community structure of networks from a source vertex or communities adopting fixed values of model's parameters. Experimental results show that the proposed methods are efficient and well-behaved in both real-world and synthetic networks

Community Detection in Quantum Complex Networks

Determining community structure is a central topic in the study of complex networks, be it technological, social, biological or chemical, in static or interacting systems. In this paper, we extend the concept of community detection from classical to quantum systems---a crucial missing component of a theory of complex networks based on quantum mechanics. We demonstrate that certain quantum mechanical effects cannot be captured using current classical complex network tools and provide new methods that overcome these problems. Our approaches are based on defining closeness measures between nodes, and then maximizing modularity with hierarchical clustering. Our closeness functions are based on quantum transport probability and state fidelity, two important quantities in quantum information theory. To illustrate the effectiveness of our approach in detecting community structure in quantum systems, we provide several examples, including a naturally occurring light-harvesting complex, LHCII. The prediction of our simplest algorithm, semiclassical in nature, mostly agrees with a proposed partitioning for the LHCII found in quantum chemistry literature, whereas our fully quantum treatment of the problem uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl

Element-centric clustering comparison unifies overlaps and hierarchy

Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In particular, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which undermine their usefulness, and no measure accommodates both overlapping and hierarchical clusterings. Here we unify the comparison of disjoint, overlapping, and hierarchically structured clusterings by proposing a new element-centric framework: elements are compared based on the relationships induced by the cluster structure, as opposed to the traditional cluster-centric philosophy. We demonstrate that, in contrast to standard clustering similarity measures, our framework does not suffer from critical biases and naturally provides unique insights into how the clusterings differ. We illustrate the strengths of our framework by revealing new insights into the organization of clusters in two applications: the improved classification of schizophrenia based on the overlapping and hierarchical community structure of fMRI brain networks, and the disentanglement of various social homophily factors in Facebook social networks. The universality of clustering suggests far-reaching impact of our framework throughout all areas of science

Community Detection in Social Networks

Social networks usually display a hierarchy of communities and it is the task of community detection algorithms to detect these communities and preferably also their hierarchical relationships. One common class of such hierarchical algorithms are the agglomerative algorithms. These algorithms start with one community per vertex in the network and keep agglomerating vertices together to form increasingly larger communities. Another common class of hierarchical algorithms are the divisive algorithms. These algorithms start with a single community comprising all the vertices of the network and then split the network into several connected components that are viewed as communities. We start this thesis by giving an introductory overview of the field of com- munity detection in part I, including complex networks, the basic groups of com- munity definitions, the modularity function, and a description of common com- munity detection techniques, including agglomerative and divisive algorithms. Then we proceed, in part II, with community detection algorithms that have been implemented and tested, with refined use of data structures, as part of this thesis. We start by describing, implementing and testing against benchmark graphs the greedy hierarchical agglomerative community detection algorithm proposed by Aaron Clauset, M. E. J. Newman, and Cristopher Moore in 2004 in the article Finding community structure in very large networks [5]. We continue with describing and implementing the hierarchical divisive algorithm proposed by Filippo Radicchi, Claudio Castellano, Federico Cecconi, Vittorio Loreto, and Domenico Parisi in 2004 in the article Defining and identifying communities in networks [28]. Instead of testing this algorithm against benchmark graphs we present a community detection web service that runs the algorithm by Radicchi et al. on the collaboration networks in the DBLP database of scientific publi- cations and co- authorships in the area of computer science. We allow the user to freely set the many parameters that we have defined for this algorithm. The final judgment on the results is measured by the modularity value or can be left to the knowledgeable user. A rough description of the design of the algorithms and of the web service is given, and all code is available at GitHub [10] [9]. Lastly, a few improvements both to the algorithm by Radicchi et al. and to the web service are presented.Master i InformatikkMAMN-INFINF39

Scaling theory of fractal complex networks

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes with which we cover the network when determining its box dimension. This approach - grounded in both scaling theory of phase transitions and renormalization group theory - leads to the consistent scaling theory of fractal complex networks, which complements the collection of scaling exponents with several new ones and reveals various relationships between them. We propose the introduction of two classes of exponents: microscopic and macroscopic, characterizing the local structure of fractal complex networks and their global properties, respectively. Interestingly, exponents from both classes are related to each other and only a few of them (three out of seven) are independent, thus bridging the local self-similarity and global scale-invariance in fractal networks. We successfully verify our findings in real networks situated in various fields (information - the World Wide Web, biological - the human brain, and social - scientific collaboration networks) and in several fractal network models.Comment: 18 pages, 7 figures; the paper is theoretical in nature; theoretical predictions have been succesfully verified in real networks (WWW, DBLP, human brain) and in several fractal network models (SHM-model, (u,v)-flowers , nested BA networks

Overcoming data scarcity of Twitter: using tweets as bootstrap with application to autism-related topic content analysis

Notwithstanding recent work which has demonstrated the potential of using Twitter messages for content-specific data mining and analysis, the depth of such analysis is inherently limited by the scarcity of data imposed by the 140 character tweet limit. In this paper we describe a novel approach for targeted knowledge exploration which uses tweet content analysis as a preliminary step. This step is used to bootstrap more sophisticated data collection from directly related but much richer content sources. In particular we demonstrate that valuable information can be collected by following URLs included in tweets. We automatically extract content from the corresponding web pages and treating each web page as a document linked to the original tweet show how a temporal topic model based on a hierarchical Dirichlet process can be used to track the evolution of a complex topic structure of a Twitter community. Using autism-related tweets we demonstrate that our method is capable of capturing a much more meaningful picture of information exchange than user-chosen hashtags.Comment: IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, 201

Link communities reveal multiscale complexity in networks

Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of networks is to identify communities: groups of related nodes that correspond to functional subunits such as protein complexes or social spheres. Communities in networks often overlap such that nodes simultaneously belong to several groups. Meanwhile, many networks are known to possess hierarchical organization, where communities are recursively grouped into a hierarchical structure. However, the fact that many real networks have communities with pervasive overlap, where each and every node belongs to more than one group, has the consequence that a global hierarchy of nodes cannot capture the relationships between overlapping groups. Here we reinvent communities as groups of links rather than nodes and show that this unorthodox approach successfully reconciles the antagonistic organizing principles of overlapping communities and hierarchy. In contrast to the existing literature, which has entirely focused on grouping nodes, link communities naturally incorporate overlap while revealing hierarchical organization. We find relevant link communities in many networks, including major biological networks such as protein-protein interaction and metabolic networks, and show that a large social network contains hierarchically organized community structures spanning inner-city to regional scales while maintaining pervasive overlap. Our results imply that link communities are fundamental building blocks that reveal overlap and hierarchical organization in networks to be two aspects of the same phenomenon.Comment: Main text and supplementary informatio

Fast Community Identification by Hierarchical Growth

A new method for community identification is proposed which is founded on the analysis of successive neighborhoods, reached through hierarchical growth from a starting vertex, and on the definition of communities as a subgraph whose number of inner connections is larger than outer connections. In order to determine the precision and speed of the method, it is compared with one of the most popular community identification approaches, namely Girvan and Newman's algorithm. Although the hierarchical growth method is not as precise as Girvan and Newman's method, it is potentially faster than most community finding algorithms.Comment: 6 pages, 5 figure