Related papers: A General Solution for Network Models with Pairwis…
A perturbation theory scheme in terms of electron hopping, which is based on the Wick theorem for Hubbard operators, is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each…
We establish new couplings among several random graph and multigraph models related to the random regular graph $G(n,d)$, including the configuration model and unions of random perfect matchings. As a main result, we verify the…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
This paper presents a novel extension of the edge-based compartmental model for epidemics with arbitrary distributions of transmission and recovery times. Using the message passing approach we also derive a new pairwise-like model for…
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning…
In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of $M$ networks (one per layer) where each is a subgraph of a foundational network $G$. Each layer network is the…
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…
Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…
A hierarchical gamma process infinite edge partition model is proposed to factorize the binary adjacency matrix of an unweighted undirected relational network under a Bernoulli-Poisson link. The model describes both homophily and stochastic…
Connections between relations in relation extraction, which we call class ties, are common. In distantly supervised scenario, one entity tuple may have multiple relation facts. Exploiting class ties between relations of one entity tuple…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
In this paper, we convert the lattice configurations into networks with different modes of links and consider models on networks with arbitrary numbers of interacting particle-pairs. We solve the Heisenberg model by revealing the relation…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…