Multi-agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of @math into a connected random @math -regular graph for some @math . Accordingly, the agents improve the robustness of the network while maintaining a similar number of links as the initial configuration by locally adding or removing some edges.
In some applications, the robustness of a graph is related to the centrality measures such as the degree, betweenness, closeness, and eigenvector centralities. Loosely speaking, the centrality measures capture the relative importances of the nodes in a graph. Detailed reviews on the centrality measures and their applications can be found in @cite_9 @cite_37 and the references therein. Typically, the perturbations applied to the nodes with higher centrality scores have a stronger impact on the overall system (e.g., @cite_26 @cite_18 @cite_21 @cite_0 ). Hence, graphs with unbalanced centrality distributions are usually vulnerable to such worst-case perturbations.
@cite_18 @cite_26 @cite_37 @cite_9 @cite_21 @cite_0
2130790725 1960177950 2127387319 1967385589 2171137858
We use measures of vertex centrality to examine interlocking directorates and their economic effects in Italy. We employ centrality measures like degree, eigenvector centrality, betweenness, and flow betweenness, along with the clustering coefficient. We document the existence of a negative relationship between both degree and eigenvector centrality and firm value. Betweenness and flow betweenness, on the other hand, are not associated with lower firm valuations. We argue that these differences derive from the different properties of these measures: while degree and eigenvector centrality measures the influence and the power of the connections, betweenness and flow betweenness are proxies for the volume of information that passes between the nodes. This result is robust with respect to the use of both stock market and operating performance measures, as well as several controlling variables. Centrality measures are used in network science to rank the relative importance of nodes and edges of a graph. Here we define new measures of centrality for power grid structure that are based on its functionality. We show that the relative importance analysis based on centrality in graph theory can be generalized to power grid network with its electrical parameters taken into account. In the paper we experiment with the proposed electrical centrality measures on the NYISO-2935 system and the IEEE 300-bus system. We analyze the centrality distribution in order to identify important nodes or branches in the system which are of essential importance in terms of system vulnerability. We also present and discuss a number of interesting discoveries regarding the importance rank of power grid nodes and branches. Abstract Egocentric centrality measures (for data on a nodes first-order zone) parallel to Freemans [Social Networks 1 (1979) 215] centrality measures for complete (sociocentric) network data are considered. Degree-based centrality is in principle identical for egocentric and sociocentric network data. A closeness measure is uninformative for egocentric data, since all geodesic distances from ego to other nodes in the first-order zone are 1 by definition. The extent to which egocentric and sociocentric versions of Freemans betweenness centrality measure correspond is explored empirically. Across seventeen diverse networks, that correspondence is found to be relatively closethough variations in egocentric network composition do lead to some notable differences in egocentric and sociocentric betweennness. The findings suggest that research design has a relatively modest impact on assessing the relative betweenness of nodes, and that a betweenness measure based on egocentric network data could be a reliable substitute for Freemans betweenness measure when it is not practical to collect complete network data. However, differences in the research methods used in sociocentric and egocentric studies could lead to additional differences in the respective betweenness centrality measures. Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness, straightness and information, are compared over 18 1-square-mile samples of different world cities. Samples are represented by primal geographic graphs, i.e., valued graphs defined by metric rather than topologic distance where intersections are turned into nodes and streets into edges. The spatial behavior of centrality indices over the networks is investigated graphically by means of color-coded maps. The results indicate that a spatial analysis, that we term multiple centrality assessment, grounded not on a single but on a set of different centrality indices, allows an extended comprehension of the city structur... Scholars are increasingly citing electronic web references which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To webcite a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its instructions for authors accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) prospectively before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted citing articles (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues A complex network can be modeled as a graph representing the ''who knows who'' relationship. In the context of graph theory for social networks, the notion of centrality is used to assess the relative importance of nodes in a given network topology. For example, in a network composed of large dense clusters connected through only a few links, the nodes involved in those links are particularly critical as far as the network survivability is concerned. This may also impact any application running on top of it. Such information can be exploited for various topological maintenance issues to prevent congestion and disruption. This can also be used offline to identify the most important actors in large social interaction graphs. Several forms of centrality have been proposed so far. Yet, they suffer from imperfections: initially designed for small social graphs, they are either of limited use (degree centrality), either incompatible in a distributed setting (e.g. random walk betweenness centrality). In this paper we introduce a novel form of centrality: the second order centrality which can be computed in a distributed manner. This provides locally each node with a value reflecting its relative criticity and relies on a random walk visiting the network in an unbiased fashion. To this end, each node records the time elapsed between visits of that random walk (called return time in the sequel) and computes the standard deviation (or second order moment) of such return times. The key point is that central nodes see regularly the random walk compared to other topology nodes. Both through theoretical analysis and simulation, we show that the standard deviation can be used to accurately identify c