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Network representation learning has aroused widespread interests in recent years. While most of the existing methods deal with edges as pairwise relationships, only a few studies have been proposed for hyper-networks to capture more…
A theory of non-homogeneous turbulence is developed and is applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics and predicts power law scalings…
A recent paper "Emergence of scaling in random networks" (cond-mat/9910332) by Barabasi and Albert proposes a growth mechanism to produce a stationary scale free distribution of the number of edges per node in large networks such as the…
We study the effect of the network topology to propagation phenomena on networks in this article. We do not assume any propagation model such as the contact process or SIR model\cite{Ker} because the study is only the consideratons of the…
Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit…
Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…
We study the structure of the load-based spanning tree (LST) that carries the maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is given by the edge-betweenness centrality, the effective number of shortest paths…
We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…
We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollob\'as et al. [2007], we show that i) the class of models is…
In this paper we generalize the Aldous-Hoover-Kallenberg theorem concerning representations of distributions of exchangeable arrays via collections of measurable maps. We give criteria when such a representation theorem exists for arrays…
Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected,…
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
Node copying is an important mechanism for network formation, yet most models assume uniform copying rules. Motivated by observations of heterogeneous triadic closure in real networks, we introduce the concept of a hidden network model - a…
Aldous-Broder algorithm is a famous algorithm used to sample a uniform spanning tree of any finite connected graph $G$, but it is more general: given an irreducible and reversible Markov chain $M$ on $G$ started at $r$, the tree rooted at…
Networks that are organized as a hierarchy of modules have been the subject of much research, mainly focusing on algorithms that can extract this community structure from data. The question of why modular hierarchical organizations are so…
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership…
Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of…