Related papers: Modulus metrics on networks
We give a necessary and sufficient graph-theoretic characterization of toric ideals of graphs that are unimodular. As a direct consequence, we provide the structure of unimodular graphs by proving that the incidence matrix of a graph $G$ is…
In this work, we define the notion of unimodular random measured metric spaces as a common generalization of various other notions. This includes the discrete cases like unimodular graphs and stationary point processes, as well as the…
The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmetric group is defined. This is then used to determine the…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
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…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
Communities are fundamental entities for the characterization of the structure of real networks. The standard approach to the identification of communities in networks is based on the optimization of a quality function known as…
Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation,…
We study the Modular Isomorphism Problem applying a combination of existing and new techniques. We make use of the small group algebra to give a positive answer for two classes of groups of nilpotency class 3. We also introduce a new…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for…
This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph…
Homophily, the tendency of individuals to connect with others who share similar attributes, is a defining feature of social networks. Understanding how groups interact, both within and across, is crucial for uncovering the dynamics of…
Random walks can reveal communities or clusters in networks, because they are more likely to stay within a cluster than leave it. Thus, one family of community detection algorithms uses random walks to measure distance between pairs of…
Collectiveness motions of crowd systems have attracted a great deal of attentions in recently years. In this paper, we try to measure the collectiveness of a crowd system by the proposed node clique learning method. The proposed method is a…
Real-world networks are often organized as modules or communities of similar nodes that serve as functional units. These networks are also rich in content, with nodes having distinguishing features or attributes. In order to discover a…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
We study the problem $\#\mathrm{EdgeSub}(\Phi)$ of counting $k$-edge subgraphs satisfying a given graph property $\Phi$ in a large host graph $G$. Building upon the breakthrough result of Curticapean, Dell and Marx (STOC 17), we express the…