Related papers: Group Vitality Indices: Axioms and Algorithms

Many empirical networks have community structure, in which nodes are densely interconnected within each community (i.e., a group of nodes) and sparsely across different communities. Like other local and meso-scale structure of networks,…

Recent publications have suggested using the Shapley value for anomaly localization for sensor data systems. Using a reasonable mathematical anomaly model for full control, experiments indicate that using a single fixed term in the Shapley…

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…

We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…

Community structure analysis is a powerful tool for social networks, which can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks obtained…

Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them,…

We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…

This paper develops computable metrics to assign priorities for information collection on network systems made up by binary components. Components are worth inspecting because their condition state is uncertain and the system functioning…

One of the most central questions in network science is: which nodes are most important? Often this question is answered using structural properties such as high connectedness or centrality in the network. However, static structural…

Borgs et al. [2016] investigated essential requirements for communities in preference networks. They defined six axioms on community functions, i.e., community detection rules. Though having elegant properties, the practicality of this…

In recent years, community structure has emerged as a key component of complex network analysis. As more data has been collected, researchers have begun investigating changing community structure across multiple networks. Several methods…

Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model…

In spite of increased attention on explainable machine learning models, explaining multi-output predictions has not yet been extensively addressed. Methods that use Shapley values to attribute feature contributions to the decision making…

The problem of assigning centrality values to nodes and edges in graphs has been widely investigated during last years. Recently, a novel measure of node centrality has been proposed, called k-path centrality index, which is based on the…

Centrality measures such as the degree, k-shell, or eigenvalue centrality can identify a network's most influential nodes, but are rarely usefully accurate in quantifying the spreading power of the vast majority of nodes which are not…

Which nodes are most vulnerable to an epidemic spreading through a network, and which carry the highest risk of causing a major outbreak if they are the source of the infection? Here we show how these questions can be answered to good…

Online social networks have become incredibly popular in recent years, which prompts an increasing number of companies to promote their brands and products through social media. This paper presents an approach for identifying influential…

Entropy measures of probability distributions are widely used measures in ecology, biology, genetics, and in other fields, to quantify species diversity of a community. Unfortunately, entropy-based diversity indices, or diversity indices…