Katz centrality

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

K-path centrality: a new centrality measure in social networks

Abstract: This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, κ-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high κ-path centrality have high node betweenness centrality. Experimental evaluations on diverse real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared to known randomized algorithms.

A novel weight neighborhood centrality algorithm for identifying influential spreaders in complex networks

Abstract: Identifying the most influential spreaders in complex networks is crucial for optimally using the network structure and designing efficient strategies to accelerate information dissemination or prevent epidemic outbreaks. In this paper, by taking into account the centrality of a node and its neighbors’ centrality which depends on the diffusion importance of links, we propose a novel influence measure, the weight neighborhood centrality, to quantify the spreading ability of nodes in complex networks. To evaluate the performance of our method, we use the Susceptible–Infected–Recovered (SIR) model to simulate the epidemic spreading process on six real-world networks and four artificial networks. By measuring the rank imprecision and the rank correlation between the rank lists generated by simulation results via SIR and the ones generated by centrality measures, it shows that in general the weight neighborhood centrality can rank the spreading ability of nodes more accurately than its benchmark centrality, especially when using the degree k or coreness k s as the benchmark centrality. Further, we compare the monotonicity and the computational complexity of different ranking methods, which show that our method not only can be better at distinguishing the spreading ability of nodes but also can be used in large-scale networks due to the high computation efficiency.

Almost linear-time algorithms for adaptive betweenness centrality using hypergraph sketches

Abstract: Betweenness centrality measures the importance of a vertex by quantifying the number of times it acts as a midpoint of the shortest paths between other vertices. This measure is widely used in network analysis. In many applications, we wish to choose the k vertices with the maximum adaptive betweenness centrality, which is the betweenness centrality without considering the shortest paths that have been taken into account by already-chosen vertices. All previous methods are designed to compute the betweenness centrality in a fixed graph. Thus, to solve the above task, we have to run these methods $k$ times. In this paper, we present a method that directly solves the task, with an almost linear runtime no matter how large the value of k. Our method first constructs a hypergraph that encodes the betweenness centrality, and then computes the adaptive betweenness centrality by examining this graph. Our technique can be utilized to handle other centrality measures. We theoretically prove that our method is very accurate, and experimentally confirm that it is three orders of magnitude faster than previous methods. Relying on the scalability of our method, we experimentally demonstrate that strategies based on adaptive betweenness centrality are effective in important applications studied in the network science and database communities.

From Structure to Activity: Using Centrality Measures to Predict Neuronal Activity.

Abstract: It is clear that the topological structure of a neural network somehow determines the activity of the neurons within it. In the present work, we ask to what extent it is possible to examine the structural features of a network and learn something about its activity? Specifically, we consider how the centrality (the importance of a node in a network) of a neuron correlates with its firing rate. To investigate, we apply an array of centrality measures, including In-Degree, Closeness, Betweenness, Eigenvector, Katz, PageRank, Hyperlink-Induced Topic Search (HITS) and NeuronRank to Leaky-Integrate and Fire neural networks with different connectivity schemes. We find that Katz centrality is the best predictor of firing rate given the network structure, with almost perfect correlation in all cases studied, which include purely excitatory and excitatory–inhibitory networks, with either homogeneous connections or a small-world structure. We identify the properties of a network which will cause this correlation to...

Fast approximation of centrality

Abstract: Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For graphs exhibiting the small world phenomenon, our method estimates the centrality of all vertices with high probability within a (1 + ∈) factor in near-linear time.