Related papers: Group Vitality Indices: Axioms and Algorithms
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
The biological roles of gene sets are used to group them into collections. These collections are often characterized by being high-dimensional, overlapping, and redundant families of sets, thus precluding a straightforward interpretation…
Influential nodes play a critical role in boosting or curbing spreading phenomena in complex networks. Numerous centrality measures have been proposed for identifying and ranking the nodes according to their importance. Classical centrality…
The selection of grouped variables using the random forest algorithm is considered. First a new importance measure adapted for groups of variables is proposed. Theoretical insights into this criterion are given for additive regression…
One key problem in network analysis is the so-called influence maximization problem, which consists in finding a set $S$ of at most $k$ seed users, in a social network, maximizing the spread of information from $S$. This paper studies a…
In this paper, we study sensitivity indices for independent groups of variables and we look at the particular case of block-additive models. We show in this case that most of the Sobol indices are equal to zero and that Shapley effects can…
We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality…
We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in the topological diversity of the assigned graphs, resulting from a resolution of their…
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
Finding "true" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster…
Variable importance measures (VIMs) aim to quantify the contribution of each input covariate to the predictability of a given output. With the growing interest in explainable AI, numerous VIMs have been proposed, many of which are heuristic…
Most research concerning the influence of network structure on phenomena taking place on the network focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though…
Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
This paper contributes to the quest for an operational definition of 'research excellence' and proposes a translation of the excellence concept into a bibliometric indicator. Starting from a textual analysis of funding program calls aimed…
The asymptotic study of the conjugacy classes of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of…
Node centrality is one of the integral measures in network analysis with wide range of applications from socio-economic to personalized recommendation. We argue that an effective centrality measure should undertake stability even under…
A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [Bonacich, 2001], measures the number of attenuated paths that exist between nodes. We introduce a normalized…
We introduce a new measure of centrality, the information centrality C^I, based on the concept of efficient propagation of information over the network. C^I is defined for both valued and non-valued graphs, and applies to groups and classes…
Centrality is a fundamental concept in network science, providing critical insights into the structure and dynamics of complex systems such as social, transportation, biological and financial networks. Despite its extensive use, there is no…