Random Walk Centrality Research Articles

Key sector analysis by IO networks: Evidence from Turkey

In this study, the key sectors of Turkey are determined using Input- Output (IO) network analysis. Different centrality measures are analyzed and compared. Accordingly, eigenvector, page rank, hub, and authority centralities are calculated. The effects of an economic shock are also analyzed using random walk centrality and counting betweenness. Findings indicate that the key sectors are ?Wholesale and Retail Trade; Repair of Motor Vehicles?, ?Transport, Storage and Communications?, ?Agriculture, Hunting and Forestry?, ?Construction?, ?Real Estate Activities?, and ?Textiles, Textile Products, Leather and Footwear?. Furthermore, the same sectors are determined to be vulnerable to economic shocks.

On fast computation of directed graph Laplacian pseudo-inverse

The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and commute times, and other connectivity measures. These measures arise in the analysis of many social and computer networks. In this short paper, we show how a linear system involving the Laplacian may be solved in time linear in the number of edges, times a factor depending on the separability of the graph. This leads directly to the column-by-column computation of the entire Laplacian pseudo-inverse in time quadratic in the number of nodes, i.e., constant time per matrix entry. The approach is based on “off-the-shelf” iterative methods for which global linear convergence is guaranteed, without recourse to any matrix elimination algorithm.

Estimating random walk centrality in networks

Random walk centrality (equivalently, the accessibility index) for the states of a time-homogeneous irreducible Markov chain on a finite state space is considered. It is known that the accessibility index for a particular state can be written in terms of the first and second moments of the first return time to that state. Based on that observation, the problem of estimating the random walk centrality of a state is approached by taking realizations of the Markov chain, and then statistically estimating the first two moments of the corresponding first return time. In addition to the estimate of the random walk centrality, this method also yields the standard error, the bias and a confidence interval for that estimate. For the case that the directed graph of the transition matrix for the Markov chain has a cut-point, an alternate strategy for computing the random walk centrality is outlined that may be of use when the centrality values are of interest for only some of the states. In order to illustrate the effectiveness of the results, estimates of the random walk centrality arising from random walks for several directed and undirected graphs are discussed.

What makes Input-Output Tables of Trade of Raw Material Goods Peculiar Networks? The World and Mexican Cases

Objective: This paper examines several peculiarities of Input-Output Tables (IOTs) of trade of raw material goods when treated as networks. Methodology: two IOTs of trade of raw material goods (World and Mexico) are compared with a network with a scale free distribution and hierarchical organization (an email database) by using distinct centralities and statistics from graph theory. Results: IOTs are a very particular type of graph due to their idiosyncrasies, for which standard graph measures cannot provide satisfactory results, and which have to be adapted to give a fragmented picture of the whole network. Recommendations: analytical tools of network theory applied to IOTs substantially improve the understanding of trade of raw material goods, both at the national and the global level, which is useful in the design of trade policy. Limitations: this research does not include random walk centrality and regime switching from external shocks. Originality: this is a novel research that enlightens the particularities of the IOTs, seen as networks, for the Mexican case. Conclusions: this investigation finds important particularities of IOTs when compared with other networks.

Multi-Attributed Graph Matching With Multi-Layer Graph Structure and Multi-Layer Random Walks.

This paper addresses the multi-attributed graph matching problem, which considers multiple attributes jointly while preserving the characteristics of each attribute for graph matching. Since most of conventional graph matching algorithms integrate multiple attributes to construct a single unified attribute in an oversimplified manner, the information from multiple attributes is often not completely utilized. In order to solve this problem, we propose a novel multi-layer graph structure that can preserve the characteristics of each attribute in separated layers, and also propose a multi-attributed graph matching algorithm based on random walk centrality with the proposed multi-layer graph structure. We compare the proposed algorithm with other state-of-the-art graph matching algorithms based on a single-layer structure using synthetic and real data sets and demonstrate the superior performance of the proposed multi-layer graph structure and the multi-attributed graph matching algorithm.

Using trajectory data to explore roadway characterization for bikeshare network

ABSTRACTThe rapid expansion of bikeshare programs nationwide provides opportunities to gain insights on the optimal development of multimodal networks and bike-friendly environments. The profusion of trajectory-level data produced by bikeshare systems allows for information extraction on users' route preferences and, if modeled properly, will lead to a greater understanding of road characteristics that are appealing to bikeshare users. Leveraging Global Positioning System (GPS) data obtained from the GREENbike program, this study proposes a method to characterize roadways (e.g. collector, peripheral road, attractive road, and local road) on the basis of a variety of network centrality functions. The methodology is able to uncover the structure of the underlying transportation network and identify locations of critical bicycle infrastructures. A series of centrality measures, including degree, shortest-path betweenness, and random-walk betweenness centrality are implemented to determine the roadway classifications. Their suitability and usability for this purpose is then explored and discussed at length through a sensitivity analysis. The method can be applied to any bikeshare system that has access to trajectory-level (i.e. GPS, crowdsourcing) data for identifying road attributes that are appealing to bike users. Results can effectively guide future investment choices.

Global industrial impact coefficient based on random walk process and inter-country input–output table

Input–output table is very comprehensive and detailed in describing the national economic system with lots of economic relationships, which contains supply and demand information among industrial sectors. The complex network, a theory and method for measuring the structure of complex system, can describe the structural characteristics of the internal structure of the research object by measuring the structural indicators of the social and economic system, revealing the complex relationship between the inner hierarchy and the external economic function. This paper builds up GIVCN-WIOT models based on World Input–Output Database in order to depict the topological structure of Global Value Chain (GVC), and assumes the competitive advantage of nations is equal to the overall performance of its domestic sectors’ impact on the GVC. Under the perspective of econophysics, Global Industrial Impact Coefficient (GIIC) is proposed to measure the national competitiveness in gaining information superiority and intermediate interests. Analysis of GIVCN-WIOT models yields several insights including the following: (1) sectors with higher Random Walk Centrality contribute more to transmitting value streams within the global economic system; (2) Half-Value Ratio can be used to measure robustness of open-economy macroeconomics in the process of globalization; (3) the positive correlation between GIIC and GDP indicates that one country’s global industrial impact could reveal its international competitive advantage.

Random walk centrality and a partition of Kemeny’s constant

We consider an accessibility index for the states of a discrete-time, ergodic, homogeneous Markov chain on a finite state space; this index is naturally associated with the random walk centrality introduced by Noh and Reiger (2004) for a random walk on a connected graph. We observe that the vector of accessibility indices provides a partition of Kemeny’s constant for the Markov chain. We provide three characterizations of this accessibility index: one in terms of the first return time to the state in question, and two in terms of the transition matrix associated with the Markov chain. Several bounds are provided on the accessibility index in terms of the eigenvalues of the transition matrix and the stationary vector, and the bounds are shown to be tight. The behaviour of the accessibility index under perturbation of the transition matrix is investigated, and examples exhibiting some counter-intuitive behaviour are presented. Finally, we characterize the situation in which the accessibility indices for all states coincide.

Spreading Effect in Industrial Complex Network Based on Revised Structural Holes Theory.

This paper analyzed the spreading effect of industrial sectors with complex network model under perspective of econophysics. Input-output analysis, as an important research tool, focuses more on static analysis. However, the fundamental aim of industry analysis is to figure out how interaction between different industries makes impacts on economic development, which turns out to be a dynamic process. Thus, industrial complex network based on input-output tables from WIOD is proposed to be a bridge connecting accurate static quantitative analysis and comparable dynamic one. With application of revised structural holes theory, flow betweenness and random walk centrality were respectively chosen to evaluate industrial sectors’ long-term and short-term spreading effect process in this paper. It shows that industries with higher flow betweenness or random walk centrality would bring about more intensive industrial spreading effect to the industrial chains they stands in, because value stream transmission of industrial sectors depends on how many products or services it can get from the other ones, and they are regarded as brokers with bigger information superiority and more intermediate interests.

Structural Investigation of Aluminum in the U.S. Economy using Network Analysis.

Metals are used in numerous products and are sourced via increasingly global and complex supply chains. Monetary input-output tables (MIOT) and network analysis can be applied to intersectoral supply chains and used to analyze structural aspects. We first provide a concise review of the literature related to network analysis applied to MIOTs. On the basis of a physical input-output table (PIOT) table of aluminum in the United States economy in 2007, we identify key sectors and discuss the overall topology of the aluminum network using tools of network analysis. Sectors highly dependent on metal product inputs or sales are identified using weighted degree centrality and their hierarchical organization is explored via clustering. Betweenness centrality and random walk centrality (page rank) are explored as means to identify network bottlenecks and relative sector importance. Aluminum, even though dominated by uses in the automobile, beverage and containers, and construction industries, finds application in a wide range of sectors. Motor vehicle parts manufacturing relies on a large number of upstream and downstream suppliers to function. We conclude by analyzing structural aspects of a subnetwork for automobile manufacturing and discuss how the use of network analysis relates to current criticality analyses of metal and mineral resources.

Random walk centrality in interconnected multilayer networks

Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in many fields, from economics to biology and from urban planning to social sciences, to identify the most (or the less) influent nodes in a network using centrality measures. However, defining the centrality of actors in interconnected complex networks is not trivial. In this paper, we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies, and extend two well known random walk centrality measures, the random walk betweenness and closeness centrality, to interconnected multilayer networks. For each of the measures we provide analytical expressions that completely agree with numerically results.

Random walk centrality for temporal networks

Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included.

Offshore Financial Centers in the Global Capital Network

Offshore financial centers are inextricably linked with the global flow of capital. Offshore financial centers encourage short-term investment by reducing market frictions. Lowered tax rates diminish the required expected gains from trading. This study employs data from the IMF’s Coordinated Portfolio Investment Survey to create a network that is weighted, directed and dynamic based on the portfolio investment positions of 240 countries. The aim of this article is to examine the topology of the global capital network to identify the importance of the roles played by 17 offshore financial centers over the period 2001–2011–particularly in diffusing portfolio investment throughout the network. This article employs two generalized measures of node centrality: random walk centrality and counting betweenness. These algorithms uncover the findings that some of these offshore financial centers are only well connected to a narrow range of countries, but they all perform well in their roles as capital transmitters and are thus very important to the efficient flow of capital to productive end users. While this study reveals reduced influence of offshore finance over time, it suggests that offshore financial centers may be beneficial to global welfare.

Vertex centralities in input-output networks reveal the structure of modern economies

Input-output tables describe the flows of goods and services between the sectors of an economy. These tables can be interpreted as weighted directed networks. At the usual level of aggregation, they contain nodes with strong self-loops and are almost completely connected. We derive two measures of node centrality that are well suited for such networks. Both are based on random walks and have interpretations as the propagation of supply shocks through the economy. Random walk centrality reveals the vertices most immediately affected by a shock. Counting betweenness identifies the nodes where a shock lingers longest. The two measures differ in how they treat self-loops. We apply both to data from a wide set of countries and uncover salient characteristics of the structures of these national economies. We further validate our indices by clustering according to sectors' centralities. This analysis reveals geographical proximity and similar developmental status.

Absence of depletion zone effects for the trapping reaction in complex networks

In the present work we examine in detail the formation of a depletion zone in the trapping reaction in networks, with a single perfect trap. We monitor the particle density rho(r) with respect to the distance r from the trap. We show using Monte Carlo simulations that the depletion zone is absent in regular, Erdos-Renyi (ER), and scale-free (SF) networks. The density profiles show significant differences for these cases. The particles are homogeneously distributed in regular and ER networks with the depletion effect appearing in very sparse ER networks. In SF networks we reveal the important role of the hubs, which due to their high random walk centrality are critical in the trapping reaction. In addition, the degree distribution plays a significant role in the distribution of the particles recovering the depletion zone formation for high gamma values. The mean connectivity of the network is found to play a significant role in both ER and SF networks.

Centrality measure of complex networks using biased random walks

We propose a novel centrality measure based on the dynamical properties of a biased random walk to provide a general framework for the centrality of vertex and edge in scale-free networks (SFNs). The suggested centrality unifies various centralities such as betweenness centrality (BC), load centrality (LC) and random walk centrality (RWC) when the degree, k, is relatively large. The relation between our centrality and other centralities in SFNs is clearly shown by both analytic and numerical methods. Regarding to the edge centrality, there have been few established studies in complex networks. Thus, we also provide a systematic analysis for the edge BC (LC) in SFNs and show that the distribution of edge BC satisfies a power-law. Furthermore we also show that the suggested centrality measures on real networks work very well as on the SFNs.

Enhanced predictability of hierarchical propagation in complex networks

We apply recent results on the dynamics of random walkers to the analysis of idealized epidemic outbreaks in scale-free networks. By replacing the node degree with the random walk centrality (RWC) we observe a refined hierarchical cascade leading to a greatly enhanced predictability for the order of infected nodes. We confirm our model results on data from real-world Internet maps at the autonomous system level. In addition we propose the RWC distribution as an additional relevant topological property of a complex network. The present results are highly relevant for the understanding of information flow in scale-free networks and the development of dynamic and adaptive strategies that aim to mitigate network attacks.

Interacting Particle Systems in Complex Networks

motion of a random walker on heterogeneous complex networks. We find that the random walker is attracted toward nodes with larger degree and that the random walk motion is asymmetric. The asymmetry can be quantified with the random walk centrality, the matrix formulation of which is presented. As an interacting system, we consider the zero-range process on complex networks. We find that a structural heterogeneity can lead to a condensation phenomenon. These studies show that structural heterogeneity plays an important role in understanding the properties of dynamical systems.

Random walks on complex networks.

We investigate random walks on complex networks and derive an exact expression for the mean first-passage time (MFPT) between two nodes. We introduce for each node the random walk centrality C, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction.