Graph Metrics for Temporal Networks

A new measure of node centrality on schedule-based space-time networks for the designation of spread potential

Node centrality is one of the most frequently revisited network theoretical concepts, which got many calculation method alternatives, each of them being conceived on different empirical or theoretical network abstractions. The vast majority of centrality measures produced up to date were conceived on static network abstractions (the so-called "snapshot" networks), which arguably are less realistic than dynamic (temporal) network abstractions. The new, temporal node centrality measure that we offer with this article, is based on an uncommon abstraction, of a space-time network derived from service schedules (timetables). The proposed measure was designed to rank nodes of a space-time network based on their spread or transmission potential, and was subsequently implemented on the network of sea ferry transportation derived from the aggregated schedules for sea ferry liner shipping services in Europe, as they occurred in the month of August, 2015. The main feature of our measure, named "the Spread Potential", is the evaluation of the potential of a node in the network for transmitting disease, information (e.g. rumours or false news), as well as other phenomena, whichever support a space-time network abstraction from regular and scheduled services with some known carrying capacities. Such abstractions are, for instance, of the transportation networks (e.g. of airline or maritime shipping or the wider logistics (delivery) networks), networks of medical (hospital) services, educational (teaching) services, and virtually, of any other scheduled networked phenomenon. The article also offers the perspectives of the measure's applicability on the non-scheduled space-time network abstractions.

Analysing dynamic work systems using DynEAST: a demonstration of concept

The capability of current Ergonomics methods to capture dynamism is limited, stifling our understanding of work-as-done, distributed situational awareness and organisational drift. This paper provides a demonstration of concept of DynEAST; an extension of the EAST framework underpinned by principles from Dynamic Network Analysis, to capture elements of dynamism within work systems. The DynEAST concept is applied to a railway maintenance case study. Case study findings demonstrate how DynEAST outputs can be used to advance our understanding of the aforementioned phenomena and better equip practitioners for current and future Ergonomics challenges.Practitioner summary: This paper introduces the DynEAST method. DynEAST enables HF/E practitioners to model and analyse dynamic features of complex work systems. The development of DynEAST is timely due to the concurrent proliferation of increasingly complex sociotechnical systems and stagnation of HF/E methods development; particularly those able to model systemic dynamism. Abbreviations: DynEAST: dynamic event analysis of systemic teamwork; EAST: dynamic event analysis of systemic teamwork; HF/E: human factors and ergonomics; HF: human factors; DNA: dynamic network analysis; HTA: hierarchal task analysis; CWA: cognitive work analysis; CAST: causal analysis based on system theory; STAMP: system theoretic accident model and processes; FRAM: functional resonance analysis method; SNA: social network analysis; DSA: distributed situational awareness; PPO: possession protection officer; PO: protection officer; RTS: railway track signals; LPA: local possession authority; SMEs: subject matter experts.

Computing top-k temporal closeness in temporal networks

The closeness centrality of a vertex in a classical static graph is the reciprocal of the sum of the distances to all other vertices. However, networks are often dynamic and change over time. Temporal distances take these dynamics into account. In this work, we consider the harmonic temporal closeness with respect to the shortest duration distance. We introduce an efficient algorithm for computing the exact top-k temporal closeness values and the corresponding vertices. The algorithm can be generalized to the task of computing all closeness values. Furthermore, we derive heuristic modifications that perform well on real-world data sets and drastically reduce the running times. For the case that edge traversal takes an equal amount of time for all edges, we lift two approximation algorithms to the temporal domain. The algorithms approximate the transitive closure of a temporal graph (which is an essential ingredient for the top-k algorithm) and the temporal closeness for all vertices, respectively, with high probability. We experimentally evaluate all our new approaches on real-world data sets and show that they lead to drastically reduced running times while keeping high quality in many cases. Moreover, we demonstrate that the top-k temporal and static closeness vertex sets differ quite largely in the considered temporal networks.

An efficient procedure for mining egocentric temporal motifs

Temporal graphs are structures which model relational data between entities that change over time. Due to the complex structure of data, mining statistically significant temporal subgraphs, also known as temporal motifs, is a challenging task. In this work, we present an efficient technique for extracting temporal motifs in temporal networks. Our method is based on the novel notion of egocentric temporal neighborhoods, namely multi-layer structures centered on an ego node. Each temporal layer of the structure consists of the first-order neighborhood of the ego node, and corresponding nodes in sequential layers are connected by an edge. The strength of this approach lies in the possibility of encoding these structures into a unique bit vector, thus bypassing the problem of graph isomorphism in searching for temporal motifs. This allows our algorithm to mine substantially larger motifs with respect to alternative approaches. Furthermore, by bringing the focus on the temporal dynamics of the interactions of a specific node, our model allows to mine temporal motifs which are visibly interpretable. Experiments on a number of complex networks of social interactions confirm the advantage of the proposed approach over alternative non-egocentric solutions. The egocentric procedure is indeed more efficient in revealing similarities and discrepancies among different social environments, independently of the different technologies used to collect data, which instead affect standard non-egocentric measures.

Dynamic measures for transportation networks

Most complex network analyses of transportation systems use simplified static representations obtained from existing connections in a time horizon. In static representations, travel times, waiting times and compatibility of schedules are neglected, thus losing relevant information. To obtain a more accurate description of transportation networks, we use a dynamic representation that considers synced paths and that includes waiting times to compute shortest paths. We use the shortest paths to define dynamic network, node and edge measures to analyse the topology of transportation networks, comparable with measures obtained from static representations. We illustrate the application of these measures with a toy model and a real transportation network built from schedules of a low-cost carrier. Results show remarkable differences between measures of static and dynamic representations, demonstrating the limitations of the static representation to obtain accurate information of transportation networks.

Unspoken Assumptions in Multi-layer Modularity maximization

A principled approach to recover communities in social networks is to find a clustering of the network nodes into modules (i.e groups of nodes) for which the modularity over the network is maximal. This guarantees partitioning the network nodes into sparsely connected groups of densely connected nodes. A popular extension of modularity has been proposed in the literature so it applies to multi-layer networks, that is, networks that model different types/aspects of interactions among a set of actors. In this extension, a new parameter, the coupling strength ω, has been introduced to couple different copies (i.e nodes) of the same actor with specific weights across different layers. This allows two nodes that refer to the same actor to reward the modularity score with an amount proportional to ω when they appear in the same community. While this extension seems to provide an effective tool to detect communities in multi-layer networks, it is not always clear what kind of communities maximising the generalised modularity can identify in multi-layer networks and whether these communities are inclusive to all possible community structures possible to exist in multi-layer networks. In addition, it has not been thoroughly investigated yet how to interpret ω in real-world scenarios, and whether a proper tuning of ω, if exists, is enough to guarantee an accurate recoverability for different types of multi-layer community structures. In this article, we report the different ways used in the literature to tune ω. We analyse different community structures that can be recovered by maximising the generalised modularity in relation to ω. We propose different models for multi-layer communities in multiplex and time-dependent networks and test if they are recoverable by modularity-maximization community detection methods under any assignment of ω. Our main finding is that only few simple models of multi-layer communities in multiplex and time-dependent networks are recoverable by modularity maximisation methods while more complex models are not accurately recoverable under any assignment of ω.

Efficient team structures in an open-ended cooperative creativity experiment

Creativity is progressively acknowledged as the main driver for progress in all sectors of humankind's activities: arts, science, technology, business, and social policies. Nowadays, many creative processes rely on many actors collectively contributing to an outcome. The same is true when groups of people collaborate in the solution of a complex problem. Despite the critical importance of collective actions in human endeavors, few works have tackled this topic extensively and quantitatively. Here we report about an experimental setting to single out some of the key determinants of efficient teams committed to an open-ended creative task. In this experiment, dynamically forming teams were challenged to create several artworks using LEGO bricks. The growth rate of the artworks, the dynamical network of social interactions, and the interaction patterns between the participants and the artworks were monitored in parallel. The experiment revealed that larger working teams are building at faster rates and that higher commitment leads to higher growth rates. Even more importantly, there exists an optimal number of weak ties in the social network of creators that maximizes the growth rate. Finally, the presence of influencers within the working team dramatically enhances the building efficiency. The generality of the approach makes it suitable for application in very different settings, both physical and online, whenever a creative collective outcome is required.

Entropy Measures of Human Communication Dynamics

Human communication is commonly represented as a temporal social network, and evaluated in terms of its uniqueness. We propose a set of new entropy-based measures for human communication dynamics represented within the temporal social network as event sequences. Using real world datasets and random interaction series of different types we find that real human contact events always significantly differ from random ones. This human distinctiveness increases over time and by means of the proposed entropy measures, we can observe sociological processes that take place within dynamic communities.

Graphlet-orbit Transitions (GoT): A fingerprint for temporal network comparison

Given a set of temporal networks, from different domains and with different sizes, how can we compare them? Can we identify evolutionary patterns that are both (i) characteristic and (ii) meaningful? We address these challenges by introducing a novel temporal and topological network fingerprint named Graphlet-orbit Transitions (GoT). We demonstrate that GoT provides very rich and interpretable network characterizations. Our work puts forward an extension of graphlets and uses the notion of orbits to encapsulate the roles of nodes in each subgraph. We build a transition matrix that keeps track of the temporal trajectory of nodes in terms of their orbits, therefore describing their evolution. We also introduce a metric (OTA) to compare two networks when considering these matrices. Our experiments show that networks representing similar systems have characteristic orbit transitions. GoT correctly groups synthetic networks pertaining to well-known graph models more accurately than competing static and dynamic state-of-the-art approaches by over 30%. Furthermore, our tests on real-world networks show that GoT produces highly interpretable results, which we use to provide insight into characteristic orbit transitions.

Analysis of big patient mobility data for identifying medical regions, spatio-temporal characteristics and care demands of patients on the move

BACKGROUND

Patient mobility can be defined as a patient's movement or utilization of a health care service located in a place or region other than the patient's place of residence. Mobility provides freedom to patients to obtain health care from providers across regions and even countries. It is essential to monitor patient choices in order to maintain the quality standards and responsiveness of the health system, otherwise, the health system may suffer from geographic disparities in the accessibility to quality and responsive health care. In this article, we study patient mobility in a national health care system to identify medical regions, spatio-temporal and service characteristics of health care utilization, and demands for patient mobility.

METHODS

We conducted a systematic analysis of province-to-province patient mobility in Turkey from December 2009 to December 2013, which was derived from 1.2 billion health service records. We first used a flow-based regionalization method to discover functional medical regions from the patient mobility network. We compare the results of data-driven regions to designated regions of the government in order to identify the areas of mismatch between planned regional service delivery and the observed utilization in the form of patient flows. Second, we used feature selection, and multivariate flow clustering to identify spatio-temporal characteristics and health care needs of patients on the move.

RESULTS

Medical regions we derived by analyzing the patient mobility data showed strong overlap with the designated regions of the Ministry of Health. We also identified a number of regions that the regional service utilization did not match the planned service delivery. Overall, our spatio-temporal and multivariate analysis of regional and long-distance patient flows revealed strong relationship with socio-demographic and cultural structure of the society and migration patterns. Also, patient flows exhibited seasonal patterns, and yearly trends which correlate with implemented policies throughout the period. We found that policies resulted in different outcomes across the country. We also identified characteristics of long-distance flows which could help inform policy-making by assessing the needs of patients in terms of medical specialization, service level and type.

CONCLUSIONS

Our approach helped identify (1) the mismatch between regional policy and practice in health care utilization (2) spatial, temporal, health service level characteristics and medical specialties that patients seek out by traveling longer distances. Our findings can help identify the imbalance between supply and demand, changes in mobility behaviors, and inform policy-making with insights.

Achieving Accurate Automatic Sleep Staging on Manually Pre-processed EEG Data Through Synchronization Feature Extraction and Graph Metrics

Sleep staging, the process of assigning labels to epochs of sleep, depending on the stage of sleep they belong, is an arduous, time consuming and error prone process as the initial recordings are quite often polluted by noise from different sources. To properly analyze such data and extract clinical knowledge, noise components must be removed or alleviated. In this paper a pre-processing and subsequent sleep staging pipeline for the sleep analysis of electroencephalographic signals is described. Two novel methods of functional connectivity estimation (Synchronization Likelihood/SL and Relative Wavelet Entropy/RWE) are comparatively investigated for automatic sleep staging through manually pre-processed electroencephalographic recordings. A multi-step process that renders signals suitable for further analysis is initially described. Then, two methods that rely on extracting synchronization features from electroencephalographic recordings to achieve computerized sleep staging are proposed, based on bivariate features which provide a functional overview of the brain network, contrary to most proposed methods that rely on extracting univariate time and frequency features. Annotation of sleep epochs is achieved through the presented feature extraction methods by training classifiers, which are in turn able to accurately classify new epochs. Analysis of data from sleep experiments on a randomized, controlled bed-rest study, which was organized by the European Space Agency and was conducted in the "ENVIHAB" facility of the Institute of Aerospace Medicine at the German Aerospace Center (DLR) in Cologne, Germany attains high accuracy rates, over 90% based on ground truth that resulted from manual sleep staging by two experienced sleep experts. Therefore, it can be concluded that the above feature extraction methods are suitable for semi-automatic sleep staging.

New time-based model to identify the influential users in online social networks

Purpose

Users are the key players in an online social network (OSN), so the behavior of the OSN is strongly related to their behavior. User weight refers to the influence of the users on the OSN. The purpose of this paper is to propose a method to identify the user weight based on a new metric for defining the time intervals.

Design/methodology/approach

The behavior of an OSN changes over time, thus the user weight in the OSN is different in each time frame. Therefore, a good metric for estimating the user weight in an OSN depends on the accuracy of the metric used to define the time interval. New metric for defining the time intervals is based on the standard deviation and identifies that the user weight is based on a simple exponential smoothing model.

Findings

The results show that the proposed method covers the maximum behavioral changes of the OSN and is able to identify the influential users in the OSN more accurately than existing methods.

Research limitations/implications

In event detection, when a terrorist attack occurs as an event, knowing the influential users help us to know the leader of the attack. Knowing the influential user in each time interval based on this study can help us to detect communities which formed around these people. Finally, in marketing, this issue helps us to have a targeted advertising.

Practical implications

User effect is a significant issue in many OSN domain problems, such as community detection, event detection and recommender systems.

Originality/value

Previous studies do not give priority to the recent time intervals in identifying the relative importance of users. Thus, defining a metric to compute a time interval that covers the maximum changes in the network is a major shortcoming of earlier studies. Some experiments were conducted on six different data sets to test the performance of the proposed model in terms of the computed time intervals and user weights.

Countries' positions in the international global value networks: Centrality and economic performance

The international exchange of goods and services is increasingly organised along global value chains in which the various production stages are carried out at many different locations all over the world. A country can be seen as holding a central position in global trade to the extent that it is involved in a large number of economic transactions with alternative potential suppliers and has a wide access to different important markets. However, the centrality of countries' positions in the international production of goods and services may vary according to the specific stages of the production process that countries occupy. Here we adopt a network-based perspective, and propose a novel three-faceted measure of centrality that captures countries' distinct roles at the upstream, midstream, and downstream stages of the international production process. Findings suggest that rankings of countries based on our measures of centrality vary across production stages. While emerging and developing countries tend to secure central positions at upstream and midstream production stages, high-income countries tend to exert prevailing roles at downstream stages. Moreover, rankings based on our measures differ from alternative rankings obtained from traditional measures of market power simply reflecting aggregate trade values. This is especially the case within more traditional industries, such as Textiles and Apparel, in which small and less developed countries can play relevant roles at various stages of the production process.

Bursty properties revealed in large-scale brain networks with a point-based method for dynamic functional connectivity

The brain is organized into large scale spatial networks that can be detected during periods of rest using fMRI. The brain is also a dynamic organ with activity that changes over time. We developed a method and investigated properties where the connections as a function of time are derived and quantified. The point based method (PBM) presented here derives covariance matrices after clustering individual time points based upon their global spatial pattern. This method achieved increased temporal sensitivity, together with temporal network theory, allowed us to study functional integration between resting-state networks. Our results show that functional integrations between two resting-state networks predominately occurs in bursts of activity. This is followed by varying intermittent periods of less connectivity. The described point-based method of dynamic resting-state functional connectivity allows for a detailed and expanded view on the temporal dynamics of resting-state connectivity that provides novel insights into how neuronal information processing is integrated in the human brain at the level of large-scale networks.

Benchmarking Measures of Network Influence

Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures.

Temporal correlation coefficient for directed networks

Previous studies dealing with network theory focused mainly on the static aggregation of edges over specific time window lengths. Thus, most of the dynamic information gets lost. To assess the quality of such a static aggregation the temporal correlation coefficient can be calculated. It measures the overall possibility for an edge to persist between two consecutive snapshots. Up to now, this measure is only defined for undirected networks. Therefore, we introduce the adaption of the temporal correlation coefficient to directed networks. This new methodology enables the distinction between ingoing and outgoing edges. Besides a small example network presenting the single calculation steps, we also calculated the proposed measurements for a real pig trade network to emphasize the importance of considering the edge direction. The farm types at the beginning of the pork supply chain showed clearly higher values for the outgoing temporal correlation coefficient compared to the farm types at the end of the pork supply chain. These farm types showed higher values for the ingoing temporal correlation coefficient. The temporal correlation coefficient is a valuable tool to understand the structural dynamics of these systems, as it assesses the consistency of the edge configuration. The adaption of this measure for directed networks may help to preserve meaningful additional information about the investigated network that might get lost if the edge directions are ignored.

Impact of Network Activity on the Spread of Infectious Diseases through the German Pig Trade Network

The trade of livestock is an important and growing economic sector, but it is also a major factor in the spread of diseases. The spreading of diseases in a trade network is likely to be influenced by how often existing trade connections are active. The activity α is defined as the mean frequency of occurrences of existing trade links, thus 0 < α ≤ 1. The observed German pig trade network had an activity of α = 0.11, thus each existing trade connection between two farms was, on average, active at about 10% of the time during the observation period 2008–2009. The aim of this study is to analyze how changes in the activity level of the German pig trade network influence the probability of disease outbreaks, size, and duration of epidemics for different disease transmission probabilities. Thus, we want to investigate the question, whether it makes a difference for a hypothetical spread of an animal disease to transport many animals at the same time or few animals at many times. A SIR model was used to simulate the spread of a disease within the German pig trade network. Our results show that for transmission probabilities <1, the outbreak probability increases in the case of a decreased frequency of animal transports, peaking range of α from 0.05 to 0.1. However, for the final outbreak size, we find that a threshold exists such that finite outbreaks occur only above a critical value of α, which is ~0.1, and therefore in proximity of the observed activity level. Thus, although the outbreak probability increased when decreasing α, these outbreaks affect only a small number of farms. The duration of the epidemic peaks at an activity level in the range of α = 0.2–0.3. Additionally, the results of our simulations show that even small changes in the activity level of the German pig trade network would have dramatic effects on outbreak probability, outbreak size, and epidemic duration. Thus, we can conclude and recommend that the network activity is an important aspect, which should be taken into account when modeling the spread of diseases within trade networks.

Spatio-temporal networks: reachability, centrality and robustness

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to random error and systematic attack, taking a unified view of their spatial and temporal performance. We propose a model of spatio-temporal paths in time-varying spatially embedded networks which captures the property that, as in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded. Through numerical experiments on three real-world urban transport systems, we study the effect of node failure on a network's topological, temporal and spatial structure. We also demonstrate the broader applicability of this framework to three other classes of network. To identify weaknesses specific to the behaviour of a spatio-temporal system, we introduce centrality measures that evaluate the importance of a node as a structural bridge and its role in supporting spatio-temporally efficient flows through the network. This exposes the complex nature of fragility in a spatio-temporal system, showing that there is a variety of failure modes when a network is subject to systematic attacks.

Adaption of the temporal correlation coefficient calculation for temporal networks (applied to a real-world pig trade network)

The average topological overlap of two graphs of two consecutive time steps measures the amount of changes in the edge configuration between the two snapshots. This value has to be zero if the edge configuration changes completely and one if the two consecutive graphs are identical. Current methods depend on the number of nodes in the network or on the maximal number of connected nodes in the consecutive time steps. In the first case, this methodology breaks down if there are nodes with no edges. In the second case, it fails if the maximal number of active nodes is larger than the maximal number of connected nodes. In the following, an adaption of the calculation of the temporal correlation coefficient and of the topological overlap of the graph between two consecutive time steps is presented, which shows the expected behaviour mentioned above. The newly proposed adaption uses the maximal number of active nodes, i.e. the number of nodes with at least one edge, for the calculation of the topological overlap. The three methods were compared with the help of vivid example networks to reveal the differences between the proposed notations. Furthermore, these three calculation methods were applied to a real-world network of animal movements in order to detect influences of the network structure on the outcome of the different methods.

Evolutionary dynamics of time-resolved social interactions

Cooperation among unrelated individuals is frequently observed in social groups when their members combine efforts and resources to obtain a shared benefit that is unachievable by an individual alone. However, understanding why cooperation arises despite the natural tendency of individuals toward selfish behavior is still an open problem and represents one of the most fascinating challenges in evolutionary dynamics. Recently, the structural characterization of the networks in which social interactions take place has shed some light on the mechanisms by which cooperative behavior emerges and eventually overcomes the natural temptation to defect. In particular, it has been found that the heterogeneity in the number of social ties and the presence of tightly knit communities lead to a significant increase in cooperation as compared with the unstructured and homogeneous connection patterns considered in classical evolutionary dynamics. Here, we investigate the role of social-ties dynamics for the emergence of cooperation in a family of social dilemmas. Social interactions are in fact intrinsically dynamic, fluctuating, and intermittent over time, and they can be represented by time-varying networks. By considering two experimental data sets of human interactions with detailed time information, we show that the temporal dynamics of social ties has a dramatic impact on the evolution of cooperation: the dynamics of pairwise interactions favors selfish behavior.