Applications of Temporal Graph Metrics to Real-World Networks

Real world networks exhibit rich temporal information: friends are added and removed over time in online social networks; the seasons dictate the predator-prey relationship in food webs; and the propagation of a virus depends on the network of human contacts throughout the day. Recent studies have demonstrated that static network analysis is perhaps unsuitable in the study of real world network since static paths ignore time order, which, in turn, results in static shortest paths overestimating available links and underestimating their true corresponding lengths. Temporal extensions to centrality and efficiency metrics based on temporal shortest paths have also been proposed. Firstly, we analyse the roles of key individuals of a corporate network ranked according to temporal centrality within the context of a bankruptcy scandal; secondly, we present how such temporal metrics can be used to study the robustness of temporal networks in presence of random errors and intelligent attacks; thirdly, we study containment schemes for mobile phone malware which can spread via short range radio, similar to biological viruses; finally, we study how the temporal network structure of human interactions can be exploited to effectively immunise human populations. Through these applications we demonstrate that temporal metrics provide a more accurate and effective analysis of real-world networks compared to their static counterparts.Comment: 25 page

Exploiting Temporal Complex Network Metrics in Mobile Malware Containment

Malicious mobile phone worms spread between devices via short-range Bluetooth contacts, similar to the propagation of human and other biological viruses. Recent work has employed models from epidemiology and complex networks to analyse the spread of malware and the effect of patching specific nodes. These approaches have adopted a static view of the mobile networks, i.e., by aggregating all the edges that appear over time, which leads to an approximate representation of the real interactions: instead, these networks are inherently dynamic and the edge appearance and disappearance is highly influenced by the ordering of the human contacts, something which is not captured at all by existing complex network measures. In this paper we first study how the blocking of malware propagation through immunisation of key nodes (even if carefully chosen through static or temporal betweenness centrality metrics) is ineffective: this is due to the richness of alternative paths in these networks. Then we introduce a time-aware containment strategy that spreads a patch message starting from nodes with high temporal closeness centrality and show its effectiveness using three real-world datasets. Temporal closeness allows the identification of nodes able to reach most nodes quickly: we show that this scheme can reduce the cellular network resource consumption and associated costs, achieving, at the same time, a complete containment of the malware in a limited amount of time.Comment: 9 Pages, 13 Figures, In Proceedings of IEEE 12th International Symposium on a World of Wireless, Mobile and Multimedia Networks (WOWMOM '11

Investigating Bimodal Clustering in Human Mobility

We apply a simple clustering algorithm to a large dataset of cellular telecommunication records, reducing the complexity of mobile phone users' full trajectories and allowing for simple statistics to characterize their properties. For the case of two clusters, we quantify how clustered human mobility is, how much of a user's spatial dispersion is due to motion between clusters, and how spatially and temporally separated clusters are from one another.Comment: 4 pages, 2 figure

The dynamical strength of social ties in information spreading

We investigate the temporal patterns of human communication and its influence on the spreading of information in social networks. The analysis of mobile phone calls of 20 million people in one country shows that human communication is bursty and happens in group conversations. These features have opposite effects in information reach: while bursts hinder propagation at large scales, conversations favor local rapid cascades. To explain these phenomena we define the dynamical strength of social ties, a quantity that encompasses both the topological and temporal patterns of human communication

Temporal Networks

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

Modeling the scaling properties of human mobility

While the fat tailed jump size and the waiting time distributions characterizing individual human trajectories strongly suggest the relevance of the continuous time random walk (CTRW) models of human mobility, no one seriously believes that human traces are truly random. Given the importance of human mobility, from epidemic modeling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model not only accounts for the empirically observed scaling laws but also allows us to analytically predict most of the pertinent scaling exponents

Geographic constraints on social network groups

Social groups are fundamental building blocks of human societies. While our social interactions have always been constrained by geography, it has been impossible, due to practical difficulties, to evaluate the nature of this restriction on social group structure. We construct a social network of individuals whose most frequent geographical locations are also known. We also classify the individuals into groups according to a community detection algorithm. We study the variation of geographical span for social groups of varying sizes, and explore the relationship between topological positions and geographic positions of their members. We find that small social groups are geographically very tight, but become much more clumped when the group size exceeds about 30 members. Also, we find no correlation between the topological positions and geographic positions of individuals within network communities. These results suggest that spreading processes face distinct structural and spatial constraints.Comment: 10 pages, 5 figure