Closeness centrality in some splitting networks

A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A variety of measures have been proposed in the literature to quantify the robustness of networks, and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. \textit{Centrality} parameters play an important role in the field of network analysis. Numerous studies have proposed and analyzed several \textit{centrality} measures. We consider \textit{closeness centrality} which is defined as the total graph-theoretic distance to all other vertices in the graph. In this paper, closeness centrality of some splitting graphs is calculated, and exact values are obtained

Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e.g., neuroscience and climatology.Comment: 21 pages, 13 figure

Stay Awhile and Listen: User Interactions in a Crowdsourced Platform Offering Emotional Support

Internet and online-based social systems are rising as the dominant mode of communication in society. However, the public or semi-private environment under which most online communications operate under do not make them suitable channels for speaking with others about personal or emotional problems. This has led to the emergence of online platforms for emotional support offering free, anonymous, and confidential conversations with live listeners. Yet very little is known about the way these platforms are utilized, and if their features and design foster strong user engagement. This paper explores the utilization and the interaction features of hundreds of thousands of users on 7 Cups of Tea, a leading online platform offering online emotional support. It dissects the level of activity of hundreds of thousands of users, the patterns by which they engage in conversation with each other, and uses machine learning methods to find factors promoting engagement. The study may be the first to measure activities and interactions in a large-scale online social system that fosters peer-to-peer emotional support

Network Analysis with the Enron Email Corpus

We use the Enron email corpus to study relationships in a network by applying six different measures of centrality. Our results came out of an in-semester undergraduate research seminar. The Enron corpus is well suited to statistical analyses at all levels of undergraduate education. Through this note's focus on centrality, students can explore the dependence of statistical models on initial assumptions and the interplay between centrality measures and hierarchical ranking, and they can use completed studies as springboards for future research. The Enron corpus also presents opportunities for research into many other areas of analysis, including social networks, clustering, and natural language processing.Comment: in Journal of Statistics Education, Volume 23, Number 2, 201

Analysis of group evolution prediction in complex networks

In the world, in which acceptance and the identification with social communities are highly desired, the ability to predict evolution of groups over time appears to be a vital but very complex research problem. Therefore, we propose a new, adaptable, generic and mutli-stage method for Group Evolution Prediction (GEP) in complex networks, that facilitates reasoning about the future states of the recently discovered groups. The precise GEP modularity enabled us to carry out extensive and versatile empirical studies on many real-world complex / social networks to analyze the impact of numerous setups and parameters like time window type and size, group detection method, evolution chain length, prediction models, etc. Additionally, many new predictive features reflecting the group state at a given time have been identified and tested. Some other research problems like enriching learning evolution chains with external data have been analyzed as well

Using Machine Learning to Predict the Evolution of Physics Research

The advancement of science as outlined by Popper and Kuhn is largely qualitative, but with bibliometric data it is possible and desirable to develop a quantitative picture of scientific progress. Furthermore it is also important to allocate finite resources to research topics that have growth potential, to accelerate the process from scientific breakthroughs to technological innovations. In this paper, we address this problem of quantitative knowledge evolution by analysing the APS publication data set from 1981 to 2010. We build the bibliographic coupling and co-citation networks, use the Louvain method to detect topical clusters (TCs) in each year, measure the similarity of TCs in consecutive years, and visualize the results as alluvial diagrams. Having the predictive features describing a given TC and its known evolution in the next year, we can train a machine learning model to predict future changes of TCs, i.e., their continuing, dissolving, merging and splitting. We found the number of papers from certain journals, the degree, closeness, and betweenness to be the most predictive features. Additionally, betweenness increases significantly for merging events, and decreases significantly for splitting events. Our results represent a first step from a descriptive understanding of the Science of Science (SciSci), towards one that is ultimately prescriptive.Comment: 24 pages, 10 figures, 4 tables, supplementary information is include

Predicting Community Evolution in Social Networks

Nowadays, sustained development of different social media can be observed worldwide. One of the relevant research domains intensively explored recently is analysis of social communities existing in social media as well as prediction of their future evolution taking into account collected historical evolution chains. These evolution chains proposed in the paper contain group states in the previous time frames and its historical transitions that were identified using one out of two methods: Stable Group Changes Identification (SGCI) and Group Evolution Discovery (GED). Based on the observed evolution chains of various length, structural network features are extracted, validated and selected as well as used to learn classification models. The experimental studies were performed on three real datasets with different profile: DBLP, Facebook and Polish blogosphere. The process of group prediction was analysed with respect to different classifiers as well as various descriptive feature sets extracted from evolution chains of different length. The results revealed that, in general, the longer evolution chains the better predictive abilities of the classification models. However, chains of length 3 to 7 enabled the GED-based method to almost reach its maximum possible prediction quality. For SGCI, this value was at the level of 3 to 5 last periods.Comment: Entropy 2015, 17, 1-x manuscripts; doi:10.3390/e170x000x 46 page

Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and it closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known it current betweenness and resistance closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Non-monotonic betweenness behaviors are found to characterize nodes that lie close to inter-community boundaries in the studied networks