Showing papers on "Katz centrality published in 2020"

Centrality Measures in Complex Networks: A Survey.

Abstract: In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the literature. Some of these centrality measures can be computed using local information of the node, such as degree centrality and semi-local centrality measure. Others use global information of the network like closeness centrality, betweenness centrality, eigenvector centrality, Katz centrality, PageRank, and so on. In this survey, we discuss these centrality measures and the state of the art literature that includes the extension of centrality measures to different types of networks, methods to update centrality values in dynamic networks, methods to identify top-k nodes, approximation algorithms, open research problems related to the domain, and so on. The paper is concluded with a discussion on application specific centrality measures that will help to choose a centrality measure based on the network type and application requirements.

Beyond ranking nodes: Predicting epidemic outbreak sizes by network centralities.

Abstract: Identifying important nodes for disease spreading is a central topic in network epidemiology. We investigate how well the position of a node, characterized by standard network measures, can predict its epidemiological importance in any graph of a given number of nodes. This is in contrast to other studies that deal with the easier prediction problem of ranking nodes by their epidemic importance in given graphs. As a benchmark for epidemic importance, we calculate the exact expected outbreak size given a node as the source. We study exhaustively all graphs of a given size, so do not restrict ourselves to certain generative models for graphs, nor to graph data sets. Due to the large number of possible nonisomorphic graphs of a fixed size, we are limited to ten-node graphs. We find that combinations of two or more centralities are predictive (R2 scores of 0.91 or higher) even for the most difficult parameter values of the epidemic simulation. Typically, these successful combinations include one normalized spectral centrality (such as PageRank or Katz centrality) and one measure that is sensitive to the number of edges in the graph.

A two phase investment game for competitive opinion dynamics in social networks

Abstract: We propose a setting for two-phase opinion dynamics in social networks, where a node's final opinion in the first phase acts as its initial biased opinion in the second phase. In this setting, we study the problem of two camps aiming to maximize adoption of their respective opinions, by strategically investing on nodes in the two phases. A node's initial opinion in the second phase naturally plays a key role in determining the final opinion of that node, and hence also of other nodes in the network due to its influence on them. However, more importantly, this bias also determines the effectiveness of a camp's investment on that node in the second phase. In order to formalize this two-phase investment setting, we propose an extension of Friedkin-Johnsen model, and hence formulate the utility functions of the camps. We arrive at a decision parameter which can be interpreted as two-phase Katz centrality. There is a natural tradeoff while splitting the available budget between the two phases. A lower investment in the first phase results in worse initial biases in the network for the second phase. On the other hand, a higher investment in the first phase spares a lower available budget for the second phase, resulting in an inability to fully harness the influenced biases. We first analyze the non-competitive case where only one camp invests, for which we present a polynomial time algorithm for determining an optimal way to split the camp's budget between the two phases. We then analyze the case of competing camps, where we show the existence of Nash equilibrium and that it can be computed in polynomial time under reasonable assumptions. We conclude our study with simulations on real-world network datasets, in order to quantify the effects of the initial biases and the weightage attributed by nodes to their initial biases, as well as that of a camp deviating from its equilibrium strategy. Our main conclusion is that, if nodes attribute high weightage to their initial biases, it is advantageous to have a high investment in the first phase, so as to effectively influence the biases to be harnessed in the second phase.

Network broadcast analysis and control of turbulent flows

Abstract: We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time We apply this analysis to a two-dimensional decaying isotropic turbulence The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis to effectively modify the evolution of turbulent flows The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows

Centrality and Corporate Governance Decisions of Korean Chaebols : A Social Network Approach

Abstract: Almeida et al. (2011) show how Korean chaebols are formed using the critical control threshold centrality. In this paper, we take a one step further by exploring how chaebols make corporate governance decisions—going public, staying private, and being divested—after chaebol formation. We introduce the social network theory to operationalize centrality in the context of the organizational structure of a business group: specifically, the degree centrality, the Katz centrality, and the Hub/Authority centrality. We find that firms with high centrality are more likely to go public while firms with low centrality are more likely to stay private or be divested. In addition, firms invested by other group firms tend to stay private and firms without substantial equity stake in other group firms tend to be divested. Firms directly owned by the controlling family are more likely to stay private and less likely to be divested. We calibrate centrality based on the social network theory and explore how Korean chaebol system evolves for survival and prosperity.

Student Participation in Online Content-Related Discussion and Its Relation to Students’ Background Knowledge

Abstract: This paper presents two novel network methods developed for education research. These methods were used to investigate online discussions and the structure of students’ background knowledge in a blended university course for pre-service teachers (n = 11). Consequently, these measures were used for correlation analysis. The social network analysis of the online discussions was based on network roles defined using triadic motifs instead of more commonly used centrality measures. The network analysis of the background knowledge is based on the Katz centrality measure and Jaccard similarity. The results reveal that both measures have characteristic features that are typical for each student. These features, however, are not correlated when student participation is controlled for. The results show that the structure and extension of a student’s background knowledge does not explain their activity and role in online discussions. The limitations and implications of the developed methods and results are discussed.

A General Centrality Framework-Based on Node Navigability

Abstract: Centrality metrics are a popular tool in Network Science to identify important nodes within a graph. We introduce the Potential Gain as a centrality measure that unifies many walk-based centrality metrics in graphs and captures the notion of node navigability, interpreted as the property of being reachable from anywhere else (in the graph) through short walks. Two instances of the Potential Gain (called the Geometric and the Exponential Potential Gain ) are presented and we describe scalable algorithms for computing them on large graphs. We also give a proof of the relationship between the new measures and established centralities. The geometric potential gain of a node can thus be characterized as the product of its Degree centrality by its Katz centrality scores. At the same time, the exponential potential gain of a node is proved to be the product of Degree centrality by its Communicability index. These formal results connect potential gain to both the “popularity” and “similarity” properties that are captured by the above centralities.

KATZ centrality with biogeography-based optimization for influence maximization problem

Abstract: In the field of social networks, the Influence Maximization Problem (IMP) is one of the most well-known issues that have attracted many researchers in recent years. Influence Maximization (IM) means trying to find the best subset of K nodes that maximizes the number of nodes influenced by this subset. The IM is an NP-hard problem that plays an important role in viral marketing and dissemination of information. The existing solutions like greedy approaches to solving IMP do not have the efficiency and accuracy in solving the problem. In this paper, we propose a new metaheuristic algorithm based on Katz centrality with biogeography-based optimization to solve IMP in the social network. In the proposed algorithm, each habitat with the subset of K nodes is considered as the solution to the IM problem. In the proposed algorithm, the Katz centrality of each node is calculated and used as the emigration rate of each habitat. The focus of the study has been on improving the performance of the BBO algorithm by combining it with the Katz centrality. The objective was to use an enhanced meta-heuristic algorithm with measuring centrality to solve the IM problem. In the results of experiments based on different types of real-world social networks, it is well known that the proposed algorithm is more efficient, accurate, and faster than influence maximization greedy approaches.

Assessing Teacher’s Discourse Effect on Students’ Learning: A Keyword Centrality Approach

Abstract: The way that content-related keywords co-occur along a lesson seems to play an important role in concept understanding and, therefore, in students’ performance. Thus, network-like structures have been used to represent and summarize conceptual knowledge, particularly in science areas. Previous work has automated the process of producing concept networks, computed different properties of these networks, and studied the correlation of these properties with students’ achievement. This work presents an automated analysis of teachers’ concept graphs, the distribution of relevance amongst content-related keywords and how this affects students’ achievement. Particularly, we automatically extracted concept networks from transcriptions of 25 physics classes with 327 students and compute three centrality measures (CMs): PageRank, Diffusion centrality, and Katz centrality. Next, we study the relation between CMs and students’ performance using multilevel analysis. Results show that PageRank and Katz centrality significantly explain around 75% of the variance between different classes. Furthermore, the overall explained variance increased from 16% to 22% when including keyword centralities of teacher’s discourse as class-level variables. This paper shows a useful, low-cost tool for teachers to analyze and learn about how they orchestrate content-related keywords along with their speech.

Potential gain as a centrality measure

Abstract: Navigability is a distinctive features of graphs associated with artificial or natural systems whose primary goal is the transportation of information or goods. We say that a graph $\mathcal{G}$ is navigable when an agent is able to efficiently reach any target node in $\mathcal{G}$ by means of local routing decisions. In a social network navigability translates to the ability of reaching an individual through personal contacts. Graph navigability is well-studied, but a fundamental question is still open: why are some individuals more likely than others to be reached via short, friend-of-a-friend, communication chains? In this article we answer the question above by proposing a novel centrality metric called the potential gain, which, in an informal sense, quantifies the easiness at which a target node can be reached. We define two variants of the potential gain, called the geometric and the exponential potential gain, and present fast algorithms to compute them. The geometric and the potential gain are the first instances of a novel class of composite centrality metrics, i.e., centrality metrics which combine the popularity of a node in $\mathcal{G}$ with its similarity to all other nodes. As shown in previous studies, popularity and similarity are two main criteria which regulate the way humans seek for information in large networks such as Wikipedia. We give a formal proof that the potential gain of a node is always equivalent to the product of its degree centrality (which captures popularity) and its Katz centrality (which captures similarity).