Vincent A. Traag

Community detection in networks with positive and negative links.

Detecting communities in complex networks accurately is a prime challenge, preceding further analyses of network characteristics and dynamics. Until now, community detection took into account only positively valued links, while many actual networks also feature negative links. We extend an existing Potts model to incorporate negative links as well, resulting in a method similar to the clustering of signed graphs, as dealt with in social balance theory, but more general. To illustrate our method, we applied it to a network of international alliances and disputes. Using data from 1993-2001, it turns out that the world can be divided into six power blocs similar to Huntingtons civilizations, with some notable exceptions.

Exploring the mobility of mobile phone users

Mobile phone datasets allow for the analysis of human behavior on an unprecedented scale. The social network, temporal dynamics and mobile behavior of mobile phone users have often been analyzed independently from each other using mobile phone datasets. In this article, we explore the connections between various features of human behavior extracted from a large mobile phone dataset. Our observations are based on the analysis of communication data of 100,000 anonymized and randomly chosen individuals in a dataset of communications in Portugal. We show that clustering and principal component analysis allow for a significant dimension reduction with limited loss of information. The most important features are related to geographical location. In particular, we observe that most people spend most of their time at only a few locations. With the help of clustering methods, we then robustly identify home and office locations and compare the results with official census data. Finally, we analyze the geographic spread of users’ frequent locations and show that commuting distances can be reasonably well explained by a gravity model.

Social Event Detection in Massive Mobile Phone Data Using Probabilistic Location Inference

The unprecedented amount of data from mobile phones creates new possibilities to analyze various aspects of human behavior. Over the last few years, much effort has been devoted to studying the mobility patterns of humans. In this paper we will focus on unusually large gatherings of people, i.e. unusual social events. We introduce the methodology of detecting such social events in massive mobile phone data, based on a Bayesian location inference framework. More specifically, we also develop a framework for deciding who is attending an event. We demonstrate the method on a few examples. Finally, we discuss some possible future approaches for event detection, and some possible analyses of the detected social events.

Dynamical Models Explaining Social Balance and Evolution of Cooperation

Social networks with positive and negative links often split into two antagonistic factions. Examples of such a split abound: revolutionaries versus an old regime, Republicans versus Democrats, Axis versus Allies during the second world war, or the Western versus the Eastern bloc during the Cold War. Although this structure, known as social balance, is well understood, it is not clear how such factions emerge. An earlier model could explain the formation of such factions if reputations were assumed to be symmetric. We show this is not the case for non-symmetric reputations, and propose an alternative model which (almost) always leads to social balance, thereby explaining the tendency of social networks to split into two factions. In addition, the alternative model may lead to cooperation when faced with defectors, contrary to the earlier model. The difference between the two models may be understood in terms of the underlying gossiping mechanism: whereas the earlier model assumed that an individual adjusts his opinion about somebody by gossiping about that person with everybody in the network, we assume instead that the individual gossips with that person about everybody. It turns out that the alternative model is able to lead to cooperative behaviour, unlike the previous model.

Significant Scales in Community Structure

Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem shows foremost in multi-resolution methods. We here introduce an efficient method for scanning for resolutions in one such method. Additionally, we introduce the notion of “significance” of a partition, based on subgraph probabilities. Significance is independent of the exact method used, so could also be applied in other methods, and can be interpreted as the gain in encoding a graph by making use of a partition. Using significance, we can determine “good” resolution parameters, which we demonstrate on benchmark networks. Moreover, optimizing significance itself also shows excellent performance. We demonstrate our method on voting data from the European Parliament. Our analysis suggests the European Parliament has become increasingly ideologically divided and that nationality plays no role.

Trading Communities, the Networked Structure of International Relations and the Kantian Peace

The authors argue that theories regarding the relationship between trade and conflict could benefit greatly from accounting for the networked structure of international trade. Indirect trade relations reduce the probability of conflict by creating (1) opportunity costs of conflict beyond those reflected by direct trade ties and (2) negative externalities for the potential combatants’ trading partners, giving them an incentive to prevent the conflict. Trade flows create groups of states with relatively dense trade ties, which we call trading communities. Within these groups, the interruptions to trade caused by conflict create relatively large costs. As a result, joint members of trading communities are less likely to go to war; however little they directly trade with each other. The authors systematically measure and define trading communities across various levels of aggregation using the network analytic tool of modularity maximization. The authors find significant support for their hypothesis, indicating that interdependence theory can be extended to extra-dyadic relations.

Detecting communities using asymptotical surprise.

Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well-known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity and may find communities where modularity fails to discern any structure.

Exponential ranking: taking into account negative links

Networks have attracted a great deal of attention the last decade, and play an important role in various scientific disciplines. Ranking nodes in such networks, based on for example PageRank or eigenvector centrality, remains a hot topic. Not only does this have applications in ranking web pages, it also allows peer-to-peer systems to have effective notions of trust and reputation and enables analyses of various (social) networks. Negative links however, confer distrust or dislike as opposed to positive links, and are usually not taken into account. In this paper we propose a ranking method we call exponential ranking, which allows for negative links in the network. We show convergence of the method, and demonstrate that it takes into account negative links effectively.

Detecting Communities through Network Data

Social life coalesces into communities through cooperation and conflict. As a case in point, Shwed and Bearman (2010) studied consensus and contention in scientific communities. They used a sophisticated modularity method to detect communities on the basis of scientific citations, which they then interpreted as directed positive network ties. They assumed that a lack of citations implies disagreement. Some scientific citations, however, are contentious and should therefore be represented by negative ties, like conflicting relations in general. After expanding the modularity method to incorporate negative ties, we show that a small proportion of negative ties, commonly present in science, is sufficient to significantly alter the community structure. In addition, our research suggests that without distinguishing negative ties, scientific communities actually represent specialized subfields, not contentious groups. Finally, we cast doubt on the assumption that lack of cites would signal disagreement. To show the general importance of discerning negative ties for understanding conflict and its impact on communities, we also analyze a public debate.

Indirect reciprocity through gossiping can lead to cooperative clusters

Explaining how cooperation can emerge, and persist over time in various species is a prime challenge for both biologists and social scientists. Whereas cooperation in non-human species might be explained through mechanisms such as kinship selection or reciprocity, this is usually regarded as insufficient to explain the extent of cooperation observed in humans. It has been theorized that indirect reciprocity—I help you, and someone else later helps me—could explain the breadth of human cooperation. Reputation is central to this idea, since it conveys important information to third parties whether to cooperate or not with a focal player. In this paper we analyze a model for reputation dynamics through gossiping, and pay specific attention to the possible cooperation networks that may arise. We show that gossiping agents can organize into cooperative clusters, i.e. cooperate within clusters, and defect between them, which can be regarded as socially balanced. We also deduce conditions for these gossiping cooperators to be evolutionary stable.