Identifying influential nodes in a network is a fundamental issue due to its wide applications, such as accelerating information diffusion or halting virus spreading. Many measures based on the network topology have emerged over the years to identify influential nodes such as Betweenness, Closeness, and Eigenvalue centrality. However, although most real-world networks are modular, few measures exploit this property. Recent works have shown that it has a significant effect on the dynamics on networks. In a modular network, a node has two types of influence: a local influence (on the nodes of its community) through its intra-community links and a global influence (on the nodes in other communities) through its inter-community links. Depending of the strength of the community structure, these two components are more or less influential. Based on this idea, we propose to extend all the standard centrality measures defined for networks with no community structure to modular networks. The so-called "Modular centrality" is a two dimensional vector. Its first component quantifies the local influence of a node in its community while the second component quantifies its global influence on the other communities of the network. In order to illustrate the effectiveness of the Modular centrality extensions, comparison with their scalar counterpart are performed in an epidemic process setting. Simulation results using the Susceptible-Infected-Recovered (SIR) model on synthetic networks with controlled community structure allows getting a clear idea about the relation between the strength of the community structure and the major type of influence (global local). Furthermore, experiments on real-world networks demonstrate the merit of this approach.
In @cite_29 , M. propose to redefine the standard centrality measures in order to characterize the influence of Western artist. Based on the idea that influential artists have connections beyond their artistic movement, they propose to define the centrality of modular networks by considering only the inter-community links. In other words, an influential artist must be related to multiple communities, rather than being strongly embedded in its own community. Considering a painter collaboration network where edges between nodes represent biographical connections between artists, they compared Betweenness and Closeness centrality measures with their classical version. Results show that the correlation values between the standard and modified centrality measures are quite high. However, the modified centrality measures allows to highlight influential nodes who might have been missed as they do not necessary rank high in the standard measures.
@cite_29
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In this work we look at the structure of the influences between Western art painters as revealed by their biographies on Wikipedia. We use a modified version of modularity maximisation with metadata to detect a partition of artists into communities based on their artistic genre and school in which they belong. We then use this community structure to discuss how influential artists reached beyond their own communities and had a lasting impact on others, by proposing modifications on standard centrality measures. Many studies on coauthorship networks focus on network topology and network statistical mechanics. This article takes a different approach by studying micro-level network properties with the aim of applying centrality measures to impact analysis. Using coauthorship data from 16 journals in the field of library and information science (LIS) with a time span of 20 years (1988–2007), we construct an evolving coauthorship network and calculate four centrality measures (closeness centrality, betweenness centrality, degree centrality, and PageRank) for authors in this network. We find that the four centrality measures are significantly correlated with citation counts. We also discuss the usability of centrality measures in author ranking and suggest that centrality measures can be useful indicators for impact analysis. © 2009 Wiley Periodicals, Inc. 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. Identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance. The degree centrality method is very simple but of little relevance. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but are incapable to be applied in large-scale networks due to the computational complexity. In order to design an effective ranking method, we proposed a semi-local centrality measure as a tradeoff between the low-relevant degree centrality and other time-consuming measures. We use the Susceptible–Infected–Recovered (SIR) model to evaluate the performance by using the spreading rate and the number of infected nodes. Simulations on four real networks show that our method can well identify influential nodes.