Centrality Metric for Dynamic Networks

Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to static networks. Most networks, on the other hand, are dynamic in nature, evolving over time through the addition or deletion of nodes and edges. A popular approach to analyzing such networks represents them by a static network that aggregates all edges observed over some time period. This approach, however, under or overestimates centrality of some nodes. We address this problem by introducing a novel centrality metric for dynamic network analysis. This metric exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times. We demonstrate on an example network that the proposed metric leads to a very different ranking than analysis of an equivalent static network. We use dynamic centrality to study a dynamic citations network and contrast results to those reached by static network analysis.Comment: in KDD workshop on Mining and Learning in Graphs (MLG

Analysis and evaluation of the entropy indices of a static network structure

Although degree distribution entropy (DDE), SD structure entropy (SDSE), Wu structure entropy (WSE) and FB structure entropy (FBSE) are four static network structure entropy indices widely used to quantify the heterogeneity of a complex network, previous studies have paid little attention to their differing abilities to describe network structure. We calculate these four structure entropies for four benchmark networks and compare the results by measuring the ability of each index to characterize network heterogeneity. We find that SDSE and FBSE more accurately characterize network heterogeneity than WSE and DDE. We also find that existing benchmark networks fail to distinguish SDSE and FBSE because they cannot discriminate local and global network heterogeneity. We solve this problem by proposing an evolving caveman network that reveals the differences between structure entropy indices by comparing the sensitivities during the network evolutionary process. Mathematical analysis and computational simulation both indicate that FBSE describes the global topology variation in the evolutionary process of a caveman network, and that the other three structure entropy indices reflect only local network heterogeneity. Our study offers an expansive view of the structural complexity of networks and expands our understanding of complex network behavior.The authors would like to thank the financial support of the National Natural Science Foundation of China (71501153), Natural Science Foundation of Shaanxi Province of China (2016JQ6072), and the Foundation of China Scholarship Council (201506965039, 201606965057). (71501153 - National Natural Science Foundation of China; 2016JQ6072 - Natural Science Foundation of Shaanxi Province of China; 201506965039 - Foundation of China Scholarship Council; 201606965057 - Foundation of China Scholarship Council)Published versio

Disease spread through animal movements: a static and temporal network analysis of pig trade in Germany

Background: Animal trade plays an important role for the spread of infectious diseases in livestock populations. As a case study, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The central question is how infectious diseases can potentially spread within the system of trade contacts. We address this question by analyzing the underlying network of animal movements. Methodology/Findings: The considered pig trade dataset spans several years and is analyzed with respect to its potential to spread infectious diseases. Focusing on measurements of network-topological properties, we avoid the usage of external parameters, since these properties are independent of specific pathogens. They are on the contrary of great importance for understanding any general spreading process on this particular network. We analyze the system using different network models, which include varying amounts of information: (i) static network, (ii) network as a time series of uncorrelated snapshots, (iii) temporal network, where causality is explicitly taken into account. Findings: Our approach provides a general framework for a topological-temporal characterization of livestock trade networks. We find that a static network view captures many relevant aspects of the trade system, and premises can be classified into two clearly defined risk classes. Moreover, our results allow for an efficient allocation strategy for intervention measures using centrality measures. Data on trade volume does barely alter the results and is therefore of secondary importance. Although a static network description yields useful results, the temporal resolution of data plays an outstanding role for an in-depth understanding of spreading processes. This applies in particular for an accurate calculation of the maximum outbreak size.Comment: main text 33 pages, 17 figures, supporting information 7 pages, 7 figure

On the Marginal Cost of Road Congestion: an Evaluation Method with Application to the Paris Region

The paper analyzes the sensitivity of the marginal congestion cost on a roadway network to the level of aggregation in space, from utmost disaggregate to utmost aggregate. Simulation and aggregation are based on a static network assignment model.Marginal cost ; Road congestion ; Cost aggregation ; Congestion indicator ; Assignment model

Dynamical Properties of Interaction Data

Network dynamics are typically presented as a time series of network properties captured at each period. The current approach examines the dynamical properties of transmission via novel measures on an integrated, temporally extended network representation of interaction data across time. Because it encodes time and interactions as network connections, static network measures can be applied to this "temporal web" to reveal features of the dynamics themselves. Here we provide the technical details and apply it to agent-based implementations of the well-known SEIR and SEIS epidemiological models.Comment: 29 pages, 15 figure