Revisiting Interval Graphs for Network Science

The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear structure in the system. The generalization is an embedding of a graph onto a multi-dimensional Euclidean space and it was used by scientists to study the multi-relational complexity of ecology. However the research went out of fashion in the 1980s and was not revisited when Network Science recently expressed interests with multi-relational networks known as multiplexes. This paper studies interval graphs from the perspective of Network Science

Ideological and Temporal Components of Network Polarization in Online Political Participatory Media

Political polarization is traditionally analyzed through the ideological stances of groups and parties, but it also has a behavioral component that manifests in the interactions between individuals. We present an empirical analysis of the digital traces of politicians in politnetz.ch, a Swiss online platform focused on political activity, in which politicians interact by creating support links, comments, and likes. We analyze network polarization as the level of intra- party cohesion with respect to inter-party connectivity, finding that supports show a very strongly polarized structure with respect to party alignment. The analysis of this multiplex network shows that each layer of interaction contains relevant information, where comment groups follow topics related to Swiss politics. Our analysis reveals that polarization in the layer of likes evolves in time, increasing close to the federal elections of 2011. Furthermore, we analyze the internal social network of each party through metrics related to hierarchical structures, information efficiency, and social resilience. Our results suggest that the online social structure of a party is related to its ideology, and reveal that the degree of connectivity across two parties increases when they are close in the ideological space of a multi-party system.Comment: 35 pages, 11 figures, Internet, Policy & Politics Conference, University of Oxford, Oxford, UK, 25-26 September 201

Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach

The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule

Community Detection in Multiplex Networks

A multiplex network models different modes of interaction among same-type entities. In this article we provide a taxonomy of community detection algorithms in multiplex networks. We characterize the different algorithms based on various properties and we discuss the type of communities detected by each method. We then provide an extensive experimental evaluation of the reviewed methods to answer three main questions: to what extent the evaluated methods are able to detect ground-truth communities, to what extent different methods produce similar community structures and to what extent the evaluated methods are scalable. One goal of this survey is to help scholars and practitioners to choose the right methods for the data and the task at hand, while also emphasizing when such choice is problematic.Comment: 55 pages. Accepted for publication on ACM Computing Surveys in a shorter versio

Multilayer Networks in a Nutshell

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's constituents. During the last two decades, network science has provided many insights in natural, social, biological and technological systems. However, real systems are more often than not interconnected, with many interdependencies that are not properly captured by single layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. We round off the review with a summary of several applications in diverse fields of science.Comment: 16 pages and 3 figures. Submitted for publicatio

Analysis of Multiplex Social Networks with R

Multiplex social networks are characterized by a common set of actors connected through multiple types of relations. The multinet package provides a set of R functions to analyze multiplex social networks within the more general framework of multilayer networks, where each type of relation is represented as a layer in the network. The package contains functions to import/export, create and manipulate multilayer networks, implementations of several state-of-the-art multiplex network analysis algorithms, e.g., for centrality measures, layer comparison, community detection and visualization. Internally, the package is mainly written in native C++ and integrated with R using the Rcpp package

Numeric Input Relations for Relational Learning with Applications to Community Structure Analysis

Most work in the area of statistical relational learning (SRL) is focussed on discrete data, even though a few approaches for hybrid SRL models have been proposed that combine numerical and discrete variables. In this paper we distinguish numerical random variables for which a probability distribution is defined by the model from numerical input variables that are only used for conditioning the distribution of discrete response variables. We show how numerical input relations can very easily be used in the Relational Bayesian Network framework, and that existing inference and learning methods need only minor adjustments to be applied in this generalized setting. The resulting framework provides natural relational extensions of classical probabilistic models for categorical data. We demonstrate the usefulness of RBN models with numeric input relations by several examples. In particular, we use the augmented RBN framework to define probabilistic models for multi-relational (social) networks in which the probability of a link between two nodes depends on numeric latent feature vectors associated with the nodes. A generic learning procedure can be used to obtain a maximum-likelihood fit of model parameters and latent feature values for a variety of models that can be expressed in the high-level RBN representation. Specifically, we propose a model that allows us to interpret learned latent feature values as community centrality degrees by which we can identify nodes that are central for one community, that are hubs between communities, or that are isolated nodes. In a multi-relational setting, the model also provides a characterization of how different relations are associated with each community

On the topology Of network fine structures

Multi-relational dynamics are ubiquitous in many complex systems like transportations, social and biological. This thesis studies the two mathematical objects that encapsulate these relationships --- multiplexes and interval graphs. The former is the modern outlook in Network Science to generalize the edges in graphs while the latter was popularized during the 1960s in Graph Theory. Although multiplexes and interval graphs are nearly 50 years apart, their motivations are similar and it is worthwhile to investigate their structural connections and properties. This thesis look into these mathematical objects and presents their connections. For example we will look at the community structures in multiplexes and learn how unstable the detection algorithms are. This can lead researchers to the wrong conclusions. Thus it is important to get formalism precise and this thesis shows that the complexity of interval graphs is an indicator to the precision. However this measure of complexity is a computational hard problem in Graph Theory and in turn we use a heuristic strategy from Network Science to tackle the problem. One of the main contributions of this thesis is the compilation of the disparate literature on these mathematical objects. The novelty of this contribution is in using the statistical tools from population biology to deduce the completeness of this thesis's bibliography. It can also be used as a framework for researchers to quantify the comprehensiveness of their preliminary investigations. From the large body of multiplex research, the thesis focuses on the statistical properties of the projection of multiplexes (the reduction of multi-relational system to a single relationship network). It is important as projection is always used as the baseline for many relevant algorithms and its topology is insightful to understand the dynamics of the system.Open Acces