Identifying experts within healthcare provider net-works is crucial for improving patient outcomes, optimizing resource allocation, and fostering medical collaboration. Traditional network-based expert detection methods primarily rely on centrality measures, which consider only structural connectivity without accounting for domain-specific expertise. In this paper, we propose a sheaf Laplacian-based expert detection method that ranks healthcare providers based on their expertise across multiple subdomains. After modeling healthcare provider networks as graphs and hypergraphs, using sheaf theory, we incorporate medical specialties into the network structure. The sheaf Laplacian diffusion model enables us to capture information propagation across providers by considering these medical specialties that facilitate a more refined ranking of experts. We evaluate our method on a benchmark dataset from the Stack Exchange healthcare community, comparing it with existing graph-based methods such as PageRank, the Susceptible-Infected-Recovered (SIR) model, and conventional Laplacian models. Experimental results using correlation and Hits@n metrics demonstrate that our sheaf-based graph and hypergraph models outperform these baselines.

Expert detection within crowdsourcing forums is crucial for enhancing content accuracy and the decision-making process, as well as identifying knowledgeable individuals on a certain topic. While current expert detection methods identify knowledgeable users effectively, these methods depend on various user behavioral statistics, which may not be available for some crowdsourcing forums, and they only recognize expert users at the forum level on a general topic, such as data science, losing specific expertise on subtopics, such as clustering. In this paper, we propose a novel method that identifies experts for each subtopic using only the user's interactions and ratings, without relying on additional user behavioral statistics. We define responding/commenting to the same post/questions as the user interaction and create graphs and hypergraphs via these interactions. Then, we define a sheaf data structure on these networks to keep each user's tag-based knowledge and connections. To model information diffusion within the network considering subtopics, we develop a novel network diffusion model via sheaf Laplacian that captures subtopic-based knowledge diffusion over the network. Furthermore, we define a new centrality method, called sheaf Laplacian centrality, to measure a given user's expertise in each subtopic. Through extensive experiments conducted on four Stack Exchange networks, we show that our models outperform baseline models in detecting subtopic-based experts.

Detecting influential users, called the influence maximization problem on social networks, is an important graph mining problem with many diverse applications such as information propagation, market advertising, and rumor controlling. There are many studies in the literature on the influential user detection problem in social networks. Although the current methods are successfully used in many different applications, they typically operate under the assumption that users are honest with one another, overlooking the role of deception in these environments. On the other hand, deception appears to be surprisingly common among humans within social networks. In this paper, we study the effect of deception in influence maximization on social networks. We begin by modeling deception within social networks and then explore opinion dynamics in these networks, incorporating deception through a recent opinion dynamics framework based on the sheaf Laplacian. We propose two methods for detecting influential nodes: sheaf Laplacian centrality and sheaf DFF centrality, both of which are designed to assess the influence of deception in the context of influence maximization. Our experimental results on synthetic and realworld networks suggest that liars are more influential than honest users in social networks. Our study underscores the potential danger and implications of deceptive practices in social network contexts.

Network analysis is an emerging field with a wide spectrum of applications across many disciplines such as social networks, computer networks, and healthcare. However, the ever-increasing size of real-world networks is a major challenge for network analysis due to their high computational and space costs. In this paper, we utilize a node similarity-based graph compression method, SGC, and investigate the effect of various node similarity measures on graph compression. SGC compresses the input graph to a smaller graph without losing any/much information about its global structure and the local proximity of its vertices. We apply our compression method to the network embedding problem to study its effectiveness and efficiency. Our experimental results on four real-world networks show that each similarity measure has a different effect on graph compression and embedding, where some yield an improvement up to 70% network embedding time without decreasing classification accuracy as evaluated on single and multi-label classification tasks.

Identifying influential nodes in a complex network is an important graph mining problem with many diverse applications such as information propagation, market advertising, and rumor controlling. Influential nodes in a network play critical roles and largely affect network structure and functions. They can diffuse or spread information throughout a complex network more rapidly. Various methods have been developed to identify important nodes to address the influential node detection problem. In this paper, we use the diffusion Fréchet function (DFF), a function that leverages network topology and is robust to noise in data, to identify the most influential nodes in networks. We apply our method to various real-world networks. We then compare its performance to the classical graph-theoretic centrality measures using the Susceptible-Infected-Recovered (SIR) simulation model. Our experimental results suggest that our method is promising in influential node detection and more effective than the classical centrality measures.

Recently, topological data analysis (TDA) that studies the shape of data by extracting its topological features has become popular in applied network science. Although recent methods show promising performance for various applications, enormous sizes of real-world networks make the existing TDA solutions for graph mining problems hard to adapt with the high computation and space costs. This paper presents a graph compression method to reduce the size of the graph while preserving homology and persistent homology, which are the popular tools in TDA. The experimental studies in real-world large-scale graphs validate the efficiency of the proposed compression method.

Recently, network embedding that encodes structural information of graphs into a vector space has become popular for network analysis. Although recent methods show promising performance for various applications, the huge size of graphs may hinder a direct application of the existing network embedding method to them. This paper presents NECL, a novel efficient Network Embedding method as answers to the following two questions: 1) Is there an ideal network Compression designed specifically for embedding? 2) Does the network compression significantly boost the network representation Learning? For the first problem, we propose a neighborhood similarity based graph compression method that compresses the input graph to a smaller graph without losing any/much information about its global structure and the local proximity of its vertices. For the second problem, we employ the compressed graph for network embedding instead of the original large graph to bring down the embedding cost. NECL is a general meta-strategy to improve the efficiency of all of the state-of-the-art graph embedding algorithms based on random walks, including DeepWalk and Node2vec, without losing their effectiveness. Extensive experiments validate the efficiency of NECL method that yields an average improvement of 23 -57% embedding time, including walking and learning time, without decreasing classification accuracy as evaluated on single and multi-label classification tasks on large real-world graphs.

Due to the growth in the number of texts and documents available online, machine learning based text classification systems are getting more popular recently. Feature extraction, converting unstructured text into a structured feature space, is one of the essential tasks for text classification. In this paper, we propose a novel feature extraction approach for text classification using the network representation of text, network topology, and machine learning techniques. We present experimental results on classifying the Holy Quran chapters based on the place each chapter was revealed to illustrate the effectiveness of the approach.

Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the rectangular braid diagram (RBD) method is proposed to compute the braid monodromy of a completely reducible n -gonal curve, i.e., the curves in the form ( y − y 1 ( x ))…( y − y n ( x ))=0, where n ∈ Z + and y i ∈ C[ x ]. Also, an algorithm is presented to compute the Alexander polynomial of these curve complements using Burau representations of braid groups. Examples for each computation are provided.