Related papers: Statistical properties of a generalized threshold …
Classical results on the statistical complexity of linear models have commonly identified the norm of the weights $\|w\|$ as a fundamental capacity measure. Generalizations of this measure to the setting of deep networks have been varied,…
We study probabilistic protocols for concurrent threshold-based load balancing in networks. There are n resources or machines represented by nodes in an undirected graph and m >> n users that try to find an acceptable resource by moving…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or…
We introduce a new percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…
We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
Bipartite Graph is often a realistic model of complex networks where two different sets of entities are involved and relationship exist only two entities belonging to two different sets. Examples include the user-item relationship of a…
Based on an expert systems approach, the issue of community detection can be conceptualized as a clustering model for networks. Building upon this further, community structure can be measured through a clustering coefficient, which is…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
The graph theoretic properties of the clustering coefficient, characteristic (or average) path length, global and local efficiency, provide valuable information regarding the structure of a graph. These four properties have applications to…