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

Ranking to Learn: Feature Ranking and Selection via Eigenvector Centrality

In an era where accumulating data is easy and storing it inexpensive, feature selection plays a central role in helping to reduce the high-dimensionality of huge amounts of otherwise meaningless data. In this paper, we propose a graph-based method for feature selection that ranks features by identifying the most important ones into arbitrary set of cues. Mapping the problem on an affinity graph-where features are the nodes-the solution is given by assessing the importance of nodes through some indicators of centrality, in particular, the Eigen-vector Centrality (EC). The gist of EC is to estimate the importance of a feature as a function of the importance of its neighbors. Ranking central nodes individuates candidate features, which turn out to be effective from a classification point of view, as proved by a thoroughly experimental section. Our approach has been tested on 7 diverse datasets from recent literature (e.g., biological data and object recognition, among others), and compared against filter, embedded and wrappers methods. The results are remarkable in terms of accuracy, stability and low execution time.Comment: Preprint version - Lecture Notes in Computer Science - Springer 201

A survey on Human Mobility and its applications

Human Mobility has attracted attentions from different fields of studies such as epidemic modeling, traffic engineering, traffic prediction and urban planning. In this survey we review major characteristics of human mobility studies including from trajectory-based studies to studies using graph and network theory. In trajectory-based studies statistical measures such as jump length distribution and radius of gyration are analyzed in order to investigate how people move in their daily life, and if it is possible to model this individual movements and make prediction based on them. Using graph in mobility studies, helps to investigate the dynamic behavior of the system, such as diffusion and flow in the network and makes it easier to estimate how much one part of the network influences another by using metrics like centrality measures. We aim to study population flow in transportation networks using mobility data to derive models and patterns, and to develop new applications in predicting phenomena such as congestion. Human Mobility studies with the new generation of mobility data provided by cellular phone networks, arise new challenges such as data storing, data representation, data analysis and computation complexity. A comparative review of different data types used in current tools and applications of Human Mobility studies leads us to new approaches for dealing with mentioned challenges

Selecting a suitable Parallel Label-propagation based algorithm for Disjoint Community Detection

Community detection is an essential task in network analysis as it helps identify groups and patterns within a network. High-speed community detection algorithms are necessary to analyze large-scale networks in a reasonable amount of time. Researchers have made significant contributions in the development of high-speed community detection algorithms, particularly in the area of label-propagation based disjoint community detection. These algorithms have been proven to be highly effective in analyzing large-scale networks in a reasonable amount of time. However, it is important to evaluate the performance and accuracy of these existing methods to determine which algorithm is best suited for a particular type of network and specific research problem. In this report, we investigate the RAK, COPRA, and SLPA, three label-propagation-based static community discovery techniques. We pay close attention to each algorithm's minute details as we implement both its single-threaded and multi-threaded OpenMP-based variants, making any necessary adjustments or optimizations and obtaining the right parameter values. The RAK algorithm is found to perform well with a tolerance of 0.05 and OpenMP-based strict RAK with 12 threads was 6.75x faster than the sequential non-strict RAK. The COPRA algorithm works well with a single label for road networks and max labels of 4-16 for other classes of graphs. The SLPA algorithm performs well with increasing memory size, but overall doesn't offer a favourable return on investment. The RAK algorithm is recommended for label-propagation based disjoint community detection.Comment: 11 pages, 1 tabl

Efficient team structures in an open-ended cooperative creativity experiment

Understanding how to best form teams to perform creative tasks is a fascinating although elusive problem. Here we propose an experimental setting for studying the performances of a population of individuals committed to an open-ended cooperative creativity task, namely the construction of LEGO artworks. The real-time parallel monitoring of the growth of the artworks and the structure and composition of the dynamically working teams allow identifying the key ingredients of successful teams. Large teams composed of committed and influential people are more effectively building. Also, there exists an optimal fraction of weak ties in the working teams, i.e., an optimal ratio exploit/explore that maximizes the building efficiency.Creativity is progressively acknowledged as the main driver for progress in all sectors of humankind{ extquoteright}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

Exploring the Evolution of Node Neighborhoods in Dynamic Networks

Dynamic Networks are a popular way of modeling and studying the behavior of evolving systems. However, their analysis constitutes a relatively recent subfield of Network Science, and the number of available tools is consequently much smaller than for static networks. In this work, we propose a method specifically designed to take advantage of the longitudinal nature of dynamic networks. It characterizes each individual node by studying the evolution of its direct neighborhood, based on the assumption that the way this neighborhood changes reflects the role and position of the node in the whole network. For this purpose, we define the concept of \textit{neighborhood event}, which corresponds to the various transformations such groups of nodes can undergo, and describe an algorithm for detecting such events. We demonstrate the interest of our method on three real-world networks: DBLP, LastFM and Enron. We apply frequent pattern mining to extract meaningful information from temporal sequences of neighborhood events. This results in the identification of behavioral trends emerging in the whole network, as well as the individual characterization of specific nodes. We also perform a cluster analysis, which reveals that, in all three networks, one can distinguish two types of nodes exhibiting different behaviors: a very small group of active nodes, whose neighborhood undergo diverse and frequent events, and a very large group of stable nodes

Centrality measures for graphons: Accounting for uncertainty in networks

As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures rely on the assumption that the graph is perfectly known -- a premise not necessarily fulfilled for large, uncertain networks. Accordingly, centrality measures may fail to faithfully extract the importance of nodes in the presence of uncertainty. To mitigate these problems, we suggest a statistical approach based on graphon theory: we introduce formal definitions of centrality measures for graphons and establish their connections to classical graph centrality measures. A key advantage of this approach is that centrality measures defined at the modeling level of graphons are inherently robust to stochastic variations of specific graph realizations. Using the theory of linear integral operators, we define degree, eigenvector, Katz and PageRank centrality functions for graphons and establish concentration inequalities demonstrating that graphon centrality functions arise naturally as limits of their counterparts defined on sequences of graphs of increasing size. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score.Comment: Authors ordered alphabetically, all authors contributed equally. 21 pages, 7 figure