Katz centrality

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

Betweenness centrality updation and community detection in streaming graphs using incremental algorithm

Abstract: Centrality measures have perpetually been helpful to find the foremost central or most powerful node within the network. There are numerous strategies to compute centrality of a node however in social networks betweenness centrality is the most widely used approach to bifurcate communities within the network, to find out the susceptibility within the complex networks and to generate the scale free networks whose degree distribution follows the power law. In this paper, we've computed betweenness centrality by identifying communities lying within the network. Our algorithm efficiently updates the centrality of the nodes whenever any edge or vertex addition or deletion takes place within the dynamic network by modifying solely a subset of vertices. For the vertex addition, Incremental Algorithm has been used in which Streaming graphs has also been considered. Brandes approach is the most widely used approach for finding out the betweenness centrality however it's still expensive for growing networks since it takes O(mn+n2logn) amount of time and O(n+m) space however our approach efficiently updates the centrality of the nodes by taking O(|S|n+|S|nlogn) amount of time where |S| is the subset of the vertices,m is the number of edges, n is the number of vertices and |S|≤n holds true.

Dependence centrality similarity: Measuring the diversity of profession levels of interests

Abstract: To understand the relations between developers and software, we study a collaborative coding platform from the perspective of networks, including follower networks, dependence networks and developer-project bipartite networks. Through the analyzing of degree distribution, PageRank and degree-dependent nearest neighbors’ centrality, we find that the degree distributions of all networks have a power-law form except the out-degree distributions of dependence networks. The nearest neighbors’ centrality is negatively correlated with degree for developers but fluctuates around the average for projects. In order to measure the diversity of profession levels of interests, a new index called dependence centrality similarity is proposed and the correlation between dependence centrality similarity and degree is investigated. The result shows an obvious negative correlations between dependence centrality similarity and degree.

On the robustness of centrality measures against link weight quantization in social networks

Abstract: In social network analysis, individuals are represented as nodes in a graph, social ties among them are represented as links, and the strength of the social ties can be expressed as link weights. However, in social network analyses where the strength of a social tie is expressed as a link weight, the link weight may be quantized to take only a few discrete values. In this paper, expressing a continuous value of social tie strength as a few discrete value is referred to as link weight quantization, and we study the effects of link weight quantization on centrality measures through simulations and experiments utilizing network generation models that generate synthetic social networks and real social network datasets. Our results show that (1) the effects of link weight quantization on the centrality measures are not significant when determining the most important node in a graph, (2) conversely, a 5---8 quantization level is needed to determine other important nodes, and (3) graphs with a highly skewed degree distribution or with a high correlation between node degree and link weights are robust against link weight quantization.

A Geometric Approach to Robustness in Complex Networks

Abstract: We explore the geometry of networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L+). The reciprocal of squared distance from each node i to the origin in this n-dimensional space yields a structural centrality index (C*(i)) for the node, while the harmonic sum of individual node structural centrality indices, Pi 1/C * (i), i.e. the trace of L+, yields the well-known Kirchoff index (K), an overall structural descriptor for the network. In addition to its geometric interpretation, we provide alternative interpretation of the proposed structural centrality index (C*(i)) of each node in terms of forced detour costs and recurrences in random walks and electrical networks. Through empirical evaluation over example and real world networks, we demonstrate how structural centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchoff index, is appropriately sensitive to perturbations/rewirings in the network.

Using Katz Centrality to Classify Multiple Pattern Transformations

Abstract: Among the many machine learning methods developed for classification tasks, the network-based learning algorithms made great success. Usually, these methods consist of two stages: the construction of a network from the original vector-based data set and the learning in the constructed network. In this paper, a network concept, called vertex centrality, is used to perform pattern classification. A group of multiple invariant transformations of a same pattern is given and the network classifier must predict the pattern class the group belongs to. The prediction is based on the Katz centrality network measurement. Due to the ability of characterizing topological structure of input patterns, the method has been shown very competitive comparing to some state-of-the-art methods.