Related papers: Modulus metrics on networks
Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately…
The structure of a social network contains information useful for predicting its evolution. Nodes that are "close" in some sense are more likely to become linked in the future than more distant nodes. We show that structural information can…
We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, that is, functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often…
The determination of node centrality is a fundamental topic in social network studies. As an addition to established metrics, which identify central nodes based on their brokerage power, the number and weight of their connections, and the…
It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem.…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
The growing popularity of online social networks has provided researchers with access to large amount of social network data. This, coupled with the ever increasing computation speed, storage capacity and data mining capabilities, led to…
As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection, probabilistic generative models (PGMs) have become the…
Modularity was introduced by Newman and Girvan in 2004 and is used as a measure of community structure of networks represented by graphs. In our work we study modularity of the random intersection graph model first considered by Karo\'nski,…
It is of paramount importance to uncover influential nodes to control diffusion phenomena in a network. In recent works, there is a growing trend to investigate the role of the community structure to solve this issue. Up to now, the vast…
Community or modular structure is considered to be a significant property of large scale real-world graphs such as social or information networks. Detecting influential clusters or communities in these graphs is a problem of considerable…
A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…
This paper addresses the ubiquity of remarkable measures on graphs, and their applications. In many queueing systems, it is necessary to take into account the compatibility constraints between users, or between supply and demands, and so…
We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…
Graph pooling is commonly applied in graph classification, yet its empirical gains over standard WL-1 expressive GNNs are often marginal or inconsistent. We study this gap by analysing the interaction between node features and graph…
We study homeomorphisms of controlled $p$-module by certain integrals. In this way, we establish various properties of mappings and show that their features are close to quasiconformal and bilipschitz mappings.
In graph-based applications, a common task is to pinpoint the most important or ``central'' vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called…