Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

Detecting community structure in social networks is a fundamental problem empowering us to identify groups of actors with similar interests. There have been extensive works focusing on finding communities in static networks, however, in reality, due to dynamic nature of social networks, they are evolving continuously. Ignoring the dynamic aspect of social networks, neither allows us to capture evolutionary behavior of the network nor to predict the future status of individuals. Aside from being dynamic, another significant characteristic of real-world social networks is the presence of leaders, i.e. nodes with high degree centrality having a high attraction to absorb other members and hence to form a local community. In this paper, we devised an efficient method to incrementally detect communities in highly dynamic social networks using the intuitive idea of importance and persistence of community leaders over time. Our proposed method is able to find new communities based on the previous structure of the network without recomputing them from scratch. This unique feature, enables us to efficiently detect and track communities over time rapidly. Experimental results on the synthetic and real-world social networks demonstrate that our method is both effective and efficient in discovering communities in dynamic social networks

Multilayer network decoding versatility and trust

In the recent years, the multilayer networks have increasingly been realized as a more realistic framework to understand emergent physical phenomena in complex real world systems. We analyze a massive time-varying social data drawn from the largest film industry of the world under multilayer network framework. The framework enables us to evaluate the versatility of actors, which turns out to be an intrinsic property of lead actors. Versatility in dimers suggests that working with different types of nodes are more beneficial than with similar ones. However, the triangles yield a different relation between type of co-actor and the success of lead nodes indicating the importance of higher order motifs in understanding the properties of the underlying system. Furthermore, despite the degree-degree correlations of entire networks being neutral, multilayering picks up different values of correlation indicating positive connotations like trust, in the recent years. Analysis of weak ties of the industry uncovers nodes from lower degree regime being important in linking Bollywood clusters. The framework and the tools used herein may be used for unraveling the complexity of other real world systems.Comment: 16 pages, 5 figure

Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to describe the spectral density of uncorrelated random graphs, much less is known about the eigenvalues of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more than a few thousand nodes is prohibitively time and memory consuming. Making use of recent advances in algorithms for spectral characterization, here we develop new methods to determine the eigenvalues of networks comparable in size to real systems, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random graphs does not converge to the semi-circle law. Furthermore, the spectral densities of real-world graphs have specific features depending on the details of the corresponding models. In particular, scale-free graphs develop a triangle-like spectral density with a power law tail, while small-world graphs have a complex spectral density function consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.Comment: 14 pages, 9 figures (corrected typos, added references) accepted for Phys. Rev.

A supervised approach for intra-/inter-community interaction prediction in dynamic social networks

Due to the growing availability of Internet services in the last decade, the interactions between people became more and more easy to establish. For example, we can have an intercontinental job interview, or we can send real-time multimedia content to any friend of us just owning a smartphone. All this kind of human activities generates digital footprints, that describe a complex, rapidly evolving, network structures. In such dynamic scenario, one of the most challenging tasks involves the prediction of future interactions between couples of actors (i.e., users in online social networks, researchers in collaboration networks). In this paper, we approach such problem by leveraging networks dynamics: to this extent, we propose a supervised learning approach which exploits features computed by time-aware forecasts of topological measures calculated between node pairs. Moreover, since real social networks are generally composed by weakly connected modules, we instantiate the interaction prediction problem in two disjoint applicative scenarios: intra-community and inter-community link prediction. Experimental results on real time-stamped networks show how our approach is able to reach high accuracy. Furthermore, we analyze the performances of our methodology when varying the typologies of features, community discovery algorithms and forecast methods

A Bayesian semi-parametric approach for modeling memory decay in dynamic social networks

In relational event networks, the tendency for actors to interact with each other depends greatly on the past interactions between the actors in a social network. Both the volume of past interactions and the time that has elapsed since the past interactions affect the actors’ decision-making to interact with other actors in the network. Recently occurred events may have a stronger influence on current interaction behavior than past events that occurred a long time ago–a phenomenon known as “memory decay”. Previous studies either predefined a short-run and long-run memory or fixed a parametric exponential memory decay using a predefined half-life period. In real-life relational event networks, however, it is generally unknown how the influence of past events fades as time goes by. For this reason, it is not recommendable to fix memory decay in an ad-hoc manner, but instead we should learn the shape of memory decay from the observed data. In this paper, a novel semi-parametric approach based on Bayesian Model Averaging is proposed for learning the shape of the memory decay without requiring any parametric assumptions. The method is applied to relational event history data among socio-political actors in India and a comparison with other relational event models based on predefined memory decays is provided

Novel Multidimensional Models of Opinion Dynamics in Social Networks

Unlike many complex networks studied in the literature, social networks rarely exhibit unanimous behavior, or consensus. This requires a development of mathematical models that are sufficiently simple to be examined and capture, at the same time, the complex behavior of real social groups, where opinions and actions related to them may form clusters of different size. One such model, proposed by Friedkin and Johnsen, extends the idea of conventional consensus algorithm (also referred to as the iterative opinion pooling) to take into account the actors' prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer a novel multidimensional extension, describing the evolution of the agents' opinions on several topics. Unlike the existing models, these topics are interdependent, and hence the opinions being formed on these topics are also mutually dependent. We rigorous examine stability properties of the proposed model, in particular, convergence of the agents' opinions. Although our model assumes synchronous communication among the agents, we show that the same final opinions may be reached "on average" via asynchronous gossip-based protocols.Comment: Accepted by IEEE Transaction on Automatic Control (to be published in May 2017