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It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be…

Weighted model integration (WMI) extends Weighted model counting (WMC) to the integration of functions over mixed discrete-continuous domains. It has shown tremendous promise for solving inference problems in graphical models and…

Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…

The topology-aware Massively Parallel Computation (MPC) model is proposed and studied recently, which enhances the classical MPC model by the awareness of network topology. The work of Hu et al. on topology-aware MPC model considers only…

When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…

Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…

We present some novel, straightforward methods for training the connection graph of a randomly initialized neural network without training the weights. These methods do not use hyperparameters defining cutoff thresholds and therefore remove…

Finding the common structural brain connectivity network for a given population is an open problem, crucial for current neuro-science. Recent evidence suggests there's a tightly connected network shared between humans. Obtaining this…

We consider fair network topology inference from nodal observations. Real-world networks often exhibit biased connections based on sensitive nodal attributes. Hence, different subpopulations of nodes may not share or receive information…

Network inference is a rapidly advancing field, with new methods being proposed on a regular basis. Understanding the advantages and limitations of different network inference methods is key to their effective application in different…

Even though the problem of network topology design is often studied as a "clean-slate" optimization, in practice most service-provider and enterprise networks are designed incrementally over time. This evolutionary process is driven by…

Despite the recent advances in developing more effective thresholding methods to convert weighted networks to unweighted counterparts, there are still several limitations that need to be addressed. One such limitation is the inability of…

The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance…

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.…

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…

Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…

Ensembles of neural networks typically outperform individual networks but incur large computational costs, whereas weight aggregation produces less costly, yet also less accurate, aggregate models. We introduce partial fusion of networks,…

It is well-known that biological and social interaction networks have a varying degree of redundancy, though a consensus of the precise cause of this is so far lacking. In this paper, we introduce a topological redundancy measure for…