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The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a group (color), we provide a framework to model multiple natural fairness aspects. We seek to find short paths in which the number of occurrences of each color is within some given lower and upper bounds. Among other results, we prove the introduced problems to be computationally intractable (NP-hard and parameterized hard with respect to the number of colors) even in very restricted settings (such as each color should appear with exactly the same frequency), while also presenting an encouraging algorithmic result ("fixed-parameter tractability") related to the length of the sought solution path for the general problem.

This paper proposes an ultra-reliable device-centric uplink (URDC-UL) communication scheme for airborne networks. In particular, base stations (BSs) are mounted on unmanned aerial vehicles (UAVs) that travel to schedule UL transmissions and collect data from devices. To attain an ultra-reliable unified device-centric performance, the UL connection is established when the UAV-BS is hovering at the nearest possible distance from the scheduled device. The performance of the proposed URDC-UL scheme is benchmarked against a stationary UAV-centric uplink (SUC-UL) scheme where the devices are scheduled to communicate to UAV-BSs that are continuously hovering at static locations. Utilizing stochastic geometry and queueing theory, novel spatiotemporal mathematical models are developed, which account for the UAV-BS spatial densities, mobility, altitude, antenna directivity, ground-to-air channel, and temporal traffic, among other factors. The results demonstrate the sensitivity of the URDC-UL scheme to the ratio between hovering and traveling time. In particular, the hovering to traveling time ratio should be carefully adjusted to maximize the harvested performance gains for the URDC-UL scheme in terms of link reliability, transmission rate, energy efficiency, and delay. Exploiting the URDC-UL scheme allows IoT devices to minimize transmission power while maintaining unified reliable transmission. This preserves the device's battery and addresses a critical IoT design challenge.

Community detection is a fundamental task in social network analysis. Online social networks have dramatically increased the volume and speed of interactions among users, enabling advanced analysis of these dynamics. Despite a growing interest in tracking the evolution of groups of users in real-world social networks, most community detection efforts focus on communities within static networks. Here, we describe a framework for tracking communities over time in a dynamic network, where a series of significant events is identified for each community. To this end, a modularity-based strategy is proposed to effectively detect and track dynamic communities. The potential of our framework is shown by conducting extensive experiments on synthetic networks containing embedded events. Results indicate that our framework outperforms other state-of-the-art methods. In addition, we briefly explore how the proposed approach can identify dynamic communities in a Twitter network composed of more than 60,000 users, which posted over 5 million tweets throughout 2020. The proposed framework can be applied to different social network and provides a valuable tool to understand the evolution of communities in dynamic social networks.

In recent years, deep convolutional neural networks (CNN) have significantly advanced face detection. In particular, lightweight CNNbased architectures have achieved great success due to their lowcomplexity structure facilitating real-time detection tasks. However, current lightweight CNN-based face detectors trading accuracy for efficiency have inadequate capability in handling insufficient feature representation, faces with unbalanced aspect ratios and occlusion. Consequently, they exhibit deteriorated performance far lagging behind the deep heavy detectors. To achieve efficient face detection without sacrificing accuracy, we design an efficient deep face detector termed EfficientFace in this study, which contains three modules for feature enhancement. To begin with, we design a novel cross-scale feature fusion strategy to facilitate bottom-up information propagation, such that fusing low-level and highlevel features is further strengthened. Besides, this is conducive to estimating the locations of faces and enhancing the descriptive power of face features. Secondly, we introduce a Receptive Field Enhancement module to consider faces with various aspect ratios. Thirdly, we add an Attention Mechanism module for improving the representational capability of occluded faces. We have evaluated EfficientFace on four public benchmarks and experimental results demonstrate the appealing performance of our method. In particular, our model respectively achieves 95.1% (Easy), 94.0% (Medium) and 90.1% (Hard) on validation set of WIDER Face dataset, which is competitive with heavyweight models with only 1/15 computational costs of the state-of-the-art MogFace detector.

A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In contrast, many essential graph classes can be recognized efficiently thanks to characterizations of the following form: there must exist an ordering of the vertices such that some ordered pattern does not appear, where a pattern is basically an ordered subgraph. These pattern characterizations have been studied for decades, but there have been recent efforts to better understand them systematically. In this paper, we focus on a simple problem at the core of this topic: given an ordered graph of size $n$, how fast can we detect whether a fixed pattern of size $k$ is present? Following the literature on graph classes recognition, we first look for patterns that can be detected in linear time. We prove, among other results, that almost all patterns on three vertices (which capture many interesting classes, such as interval, chordal, split, bipartite, and comparability graphs) fall in this category. Then, in a finer-grained complexity perspective, we prove conditional lower bounds for this problem. In particular we show that for a large family of patterns on four vertices it is unlikely that subquadratic algorithm exist. Finally, we define a parameter for patterns, the merge-width, and prove that for patterns of merge-width $t$, one can solve the problem in $O(n^{ct})$ for some constant~$c$. As a corollary, we get that detecting outerplanar patterns and other classes of patterns can be done in time independent of the size of the pattern.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.

In recent years, Graph Neural Networks (GNNs), which can naturally integrate node information and topological structure, have been demonstrated to be powerful in learning on graph data. These advantages of GNNs provide great potential to advance social recommendation since data in social recommender systems can be represented as user-user social graph and user-item graph; and learning latent factors of users and items is the key. However, building social recommender systems based on GNNs faces challenges. For example, the user-item graph encodes both interactions and their associated opinions; social relations have heterogeneous strengths; users involve in two graphs (e.g., the user-user social graph and the user-item graph). To address the three aforementioned challenges simultaneously, in this paper, we present a novel graph neural network framework (GraphRec) for social recommendations. In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed framework GraphRec. Our code is available at \url{//github.com/wenqifan03/GraphRec-WWW19}

This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both the mixing coefficients and the community distribution are parameterized by the low-dimensional representations of the nodes and communities. We designed an effective variational inference algorithm which regularizes the community membership of neighboring nodes to be similar in the latent space. Experimental results on multiple real-world graphs show that vGraph is very effective in both community detection and node representation learning, outperforming many competitive baselines in both tasks. We show that the framework of vGraph is quite flexible and can be easily extended to detect hierarchical communities.

Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.