Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community detection. Existing methods are largely focused on finding distributed representations for unsigned networks and are unable to discover embeddings that respect ...

Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks’ matrix representations to learn an embe...

This paper describes an investigation into the properties of spatially embedded complex networks representing the porous architecture of soil systems. We suggest an approach to quantify the complexity of soil pore structure based on the node-node link correlation properties of the networks. We show that the complexity depends on the strength of spatial embedding of the network and that this is ...

Fix integers d, g, r such that r ≥ 3, g > 0 and d ≥ g + r. Here we prove the existence of an integral non-special curve C in an r-dimensional projective space such that deg(C) = d, pa(C) = g, C has exactly one node and C has maximal rank (i.e. it has the expected postulation), i.e., the general non-special embedding of a general curve with a single node has maximal rank. M.S.C. 2010: 14H51, 4N05.

Network embedding is an effective way to realize the quantitative analysis of large-scale networks. However, mainstream network models are limited by manually pre-set metapaths, which leads unstable performance model. At same time, information from homogeneous neighbors mostly focused in encoding target node, while ignoring role heterogeneous node embedding. This paper proposes a new model, HeM...

Many real-world networks are described by both connectivity information and features for every node. To better model and understand these networks, we present structure preserving metric learning (SPML), an algorithm for learning a Mahalanobis distance metric from a network such that the learned distances are tied to the inherent connectivity structure of the network. Like the graph embedding a...

Graph embedding has been proven to be efficient and effective in facilitating graph analysis. In this paper, we present a novel spectral framework called NOn-Backtracking Embedding (NOBE), which offers a new perspective that organizes graph data at a deep level by tracking the flow traversing on the edges with backtracking prohibited. Further, by analyzing the non-backtracking process, a techni...

Effective visualization is vital for understanding a complex network, in particular its dynamical aspect such as information diffusion process. Existing node embedding methods are all based solely on the network topology and sometimes produce counter-intuitive visualization. A new node embedding method based on conditional probability is proposed that explicitly addresses diffusion process usin...

We present a new stochastic model for complex networks, based on a spatial embedding of the nodes, called the Spatial Preferred Attachment (SPA) model. In the SPA model, nodes have influence regions of varying size, and new nodes may only link to a node if they fall within its influence region. The spatial embedding of the nodes models the background knowledge or identity of the node, which wil...

We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a lowdimensional space, the algorithm allows us to compare networks in terms of structural similarity and to solve outstanding predictive problems. Unlike alternative approaches that focus on node level features, we lea...