Katz centrality

About: Katz centrality is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 77858 citations.

Measuring node centrality when local and global measures overlap.

Abstract: Centrality metrics aim to identify the most relevant nodes in a network. In the literature, a broad set of metrics exists, measuring either local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the usual global centrality measures typically do not add significant information with respect to the degree, i.e., the simplest local metric. To extract different information from this class of networks, we propose the use of the Generalized Economic Complexity index (GENEPY). Despite its original definition within the economic field, the GENEPY can be easily applied and interpreted on a wide range of networks, characterized by high spectral gap, including monopartite and bipartite network systems. Tests on synthetic and real-world networks show that the GENEPY can shed light about the node centrality, carrying information generally poorly correlated with the node number of direct connections (node degree).

Centrality of regions in R&D networks: Conceptual clarifications and a new measure

Abstract: This paper aims at introducing a novel measure of regional centrality in the context of R&D networks. We first demonstrate some substantial problems of SNA-based centrality measures to cope with regional R&D networks in a meaningful way. Then, we introduce a new measurement approach of regional network centrality based on the concept of inter-regional bridging paths (indirect connections at the regional level). We show that the formal definition of our regional bridging centrality measure can be expressed in terms of three simple components: the participation intensity of a region in inter-regional R&D collaborations, the relative outward orientation in terms of all established links and the diversification of R&D collaborations among partner regions. We illustrate the measure and its behaviour with respect to other conventional centrality measures by using the European co-patent network at the NUTS 2 level.

Centrality-Friendship Paradoxes: When Our Friends Are More Important Than Us

Abstract: The friendship paradox states that, on average, our friends have more friends than we do. In network terms, the average degree over the nodes can never exceed the average degree over the neighbours of nodes. This effect, which is a classic example of sampling bias, has attracted much attention in the social science and network science literature, with variations and extensions of the paradox being defined, tested and interpreted. Here, we show that a version of the paradox holds rigorously for eigenvector centrality: on average, our friends are more important than us. We then consider general matrix-function centrality, including Katz centrality, and give sufficient conditions for the paradox to hold. We also discuss which results can be generalized to the cases of directed and weighted edges. In this way, we add theoretical support for a field that has largely been evolving through empirical testing.

Correlations between Centrality Measures for Mobile Ad hoc Networks

Abstract: The author conducts an extensive correlation coefficient analysis of four prominent centrality measures for mobile ad hoc networks. The centrality measures considered are the degree-based degree centrality and eigenvector centrality, and the shortest path-based betweenness centrality and closeness centrality. The author evaluates the correlation coefficient between any two of the above four centrality measures as a function of network connectivity and node mobility. He observes a consistent ranking with respect to the correlation coefficients among the pairs of centrality measures for all levels of network connectivity, node mobility and across the duration of the simulation session. The shortest path-based closeness centrality measure exhibits high correlation with the degree-based centrality measures, whereas the betweenness centrality exhibits relatively weak correlation with the degree-based centrality measures. For a given level of node mobility and network connectivity, the author does not observe the correlation coefficient values between any two centrality measures to significantly change with time.

Inter-regional betweenness centrality in the European R&D network: Empirical investigation using European Framework data

Abstract: An overarching concern in regional science is the characterization of interactions—such as commuter flows, transport, migration, or knowledge flows—within and between subnational spatial units. In this work, we use techniques from social network analysis to address the quality, rather than the quantity, of such interactions. Given the great current interest in European RD the fraction of the shortest paths on which an edge occurs is defined as the edge betweenness centrality. Edges with high betweenness centrality have the greatest load, are strategically positioned, and potentially can act as bottlenecks for the flows. We use this idea to evaluate knowledge flows between organizations in the European R&D network, considering several ways to relate the betweenness centrality at the level of FP project participants to knowledge flows at the NUTS2 regional level. We do so by aggregating betweenness centrality values calculated using bipartite graphs linking organizations to the FP projects in which they participate, considering annual FP data between the years 1999 and 2006. We determine the most central inter-regional knowledge flows, describe how this changes over time, and consider the implications for knowledge flows in European R&D networks. We model the centrality of the flows by means of spatial interaction models, estimating how geographical, technological, and social factors influence which region pairs become bottlenecks in the flow of knowledge. The results have meaningful implications to European R&D policy, in particular concerning which region pairs constitute the core in European R&D networks and which mechanisms drive the formation of this regional core. Keywords: European R&D networks, social network analysis, betweenness centrality, Framework Programmes JEL codes: L14, O31, R12