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The modern educational ecosystem is not one-size fits all. Scholars are accustomed to personalization in their everyday life and expect the same from education systems. Additionally, the COVID-19 pandemic placed us all in an acute teaching and learning laboratory experimentation which now creates expectations of self-paced learning and interactions with focused educational materials. Consequently, we examine how learning objectives can be achieved through a learning platform that offers content choices and multiple modalities of engagement to support self-paced learning, and propose an approach to personalized education based on network science. This framework brings the attention to learning experiences, rather than teaching experiences, by providing the learner engagement and content choices supported by a network of knowledge, based on and driven by individual skills and goals. We conclude with a discussion of a prototype of such a learning platform, called CHUNK Learning.

The diversity of fifth generation (5G) network use cases, multiple access technologies, and network deployments requires measures of network robustness that complement throughput-centric error rates. In this paper, we investigate robustness in nonorthogonal multiple access (NOMA) 5G networks through temporal network theory. We develop a graph model and analytical framework to characterize time-varying network connectedness as a function of NOMA overloading. We extend our analysis to derive lower bounds and probability expressions for the number of medium access control frames required to achieve pairwise connectivity between all network devices. We support our analytical results through simulation., Comment: 11 pages, 3 figures, This paper has been accepted for the 55th Hawaii International Conference on System Sciences (HICSS-55)

Due to the extensive role of social networks in social media, it is easy for people to share the news, and it spreads faster than ever before. These platforms also have been exploited to share the rumor or fake information, which is a threat to society. One method to reduce the impact of fake information is making people aware of the correct information based on hard proof. In this work, first, we propose a propagation model called Competitive Independent Cascade Model with users' Bias (CICMB) that considers the presence of strong user bias towards different opinions, believes, or political parties. We further propose a method, called $k-TruthScore$, to identify an optimal set of truth campaigners from a given set of prospective truth campaigners to minimize the influence of rumor spreaders on the network. We compare $k-TruthScore$ with state of the art methods, and we measure their performances as the percentage of the saved nodes (nodes that would have believed in the fake news in the absence of the truth campaigners). We present these results on a few real-world networks, and the results show that $k-TruthScore$ method outperforms baseline methods., Comment: Accepted in CSoNet 2020

Do studies show that physical and online students' social networks support education? Analyzing interactions between students in schools and universities can provide a wealth of information. Studies on students' social networks can help us understand their behavioral dynamics, the correlation between their friendships and academic performance, community and group formation, information diffusion, and so on. Educational goals and holistic development of students with various academic abilities and backgrounds can be achieved by incorporating the findings attained by the studies in terms of knowledge propagation in classroom and spread of delinquent behaviors. Moreover, we use Social Network Analysis (SNA) to identify isolated students, ascertain the group study culture, analyze the spreading of various habits like smoking, drinking, and so on. In this paper, we present a review of the research showing how analysis of students' social networks can help us identify how improved educational methods can be used to make learning more inclusive at both school and university levels and achieve holistic development of students through expansion of their social networks, as well as control the spread of delinquent behaviors., Comment: Huso 2019

In many modern image-classification applications, understanding the cause of model's prediction can be as critical as the prediction's accuracy itself. Various feature-based local explanations generation methods have been designed to give us more insights on the decision of complex classifiers. Nevertheless, there is no consensus on evaluating the quality of different explanations. In response to this lack of comprehensive evaluation, we introduce the c-Eval metric and its corresponding framework to quantify the feature-based local explanation's quality. Given a classifier's prediction and the corresponding explanation on that prediction, c-Eval is the minimum-distortion perturbation that successfully alters the prediction while keeping the explanation's features unchanged. We then demonstrate how c-Eval can be computed using some modifications on existing adversarial generation libraries. To show that c-Eval captures the importance of input's features, we establish the connection between c-Eval and the features returned by explainers in affine and nearly-affine classifiers. We then introduce the c-Eval plot, which not only displays a strong connection between c-Eval and explainers' quality, but also helps automatically determine explainer's parameters. Since the generation of c-Eval relies on adversarial generation, we provide a demo of c-Eval on adversarial-robust models and show that the metric is applicable in those models. Finally, extensive experiments of explainers on different datasets are conducted to support the adoption of c-Eval in evaluating explainers' performance.

Digital forensic analysts depend on the ability to understand the social networks of the individuals they investigate. We develop a novel method for automatically constructing these networks from collected hard drives. We accomplish this by scanning the raw storage media for email addresses, constructing co-reference networks based on the proximity of email addresses to each other, then selecting connected components that correspond to real communication networks. We validate our analysis against a tagged data-set of networks for which we determined ground truth through interviews with the drive owners. In the resulting social networks, we find that classical measures of centrality and community detection algorithms are effective for identifying important nodes and close associates.

Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is $O(n \cdot m + n)$, where $n$ represents total number of nodes, and $m$ represents total number of edges in the network. In the present work, we propose a heuristic method to fast estimate the closeness rank of a node in $O(\alpha \cdot m)$ time complexity, where $\alpha = 3$. We also propose an extended improved method using uniform sampling technique. This method better estimates the rank and it has the time complexity $O(\alpha \cdot m)$, where $\alpha \approx 10-100$. This is an excellent improvement over the classical centrality ranking method. The efficiency of the proposed methods is verified on real world scale-free social networks using absolute and weighted error functions.

Most real world dynamic networks are evolved very fast with time. It is not feasible to collect the entire network at any given time to study its characteristics. This creates the need to propose local algorithms to study various properties of the network. In the present work, we estimate degree rank of a node without having the entire network. The proposed methods are based on the power law degree distribution characteristic or sampling techniques. The proposed methods are simulated on synthetic networks, as well as on real world social networks. The efficiency of the proposed methods is evaluated using absolute and weighted error functions. Results show that the degree rank of a node can be estimated with high accuracy using only $1\%$ samples of the network size. The accuracy of the estimation decreases from high ranked to low ranked nodes. We further extend the proposed methods for random networks and validate their efficiency on synthetic random networks, that are generated using Erd\H{o}s-R\'{e}nyi model. Results show that the proposed methods can be efficiently used for random networks as well.

The focus of the current research is to identify people of interest in social networks. We are especially interested in studying dark networks, which represent illegal or covert activity. In such networks, people are unlikely to disclose accurate information when queried. We present REDLEARN, an algorithm for sampling dark networks with the goal of identifying as many nodes of interest as possible. We consider two realistic lying scenarios, which describe how individuals in a dark network may attempt to conceal their connections. We test and present our results on several real-world multilayered networks, and show that REDLEARN achieves up to a 340% improvement over the next best strategy.

The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree sequence, a list of the adjacency matrix row sums. The distance matrix shows more information, namely the length of shortest paths between vertex pairs. We introduce and explore the neighborhood matrix, which we have found to be an analog to the distance matrix what the degree sequence is to the adjacency matrix. The neighbor matrix includes the degree sequence as its first column and the sequence of all other distances in the graph up to the graph's diameter, enumerating the number of neighbors each vertex has at every distance present in the graph. We prove this matrix to contain eleven oft-used graph statistics and topological descriptors. We also provide insight into two applications that show potential utility of the neighbor matrix in comparing graphs and identifying topologically significant vertices in a graph., Comment: Presented on October 17, 2015 at the Midwestern Conference on Combinatorics and Combinatoric Computing; 15 pages, 5 figures, 3 tables. Accepted for publication in the Journal of Combinatorial Mathematics and Combinatorial Computing on May 27, 2016

Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or sub-graph) detection within a network/graph, we focused on finding characterizations of k-dense communities. For each edge $uv\in E(G)$, the {\bf edge multiplicity} of $uv$ in $G$ is given by $m_G(uv)=|N_{G}(u)\cap N_{G}(v)|.$ For an integer $k$ with $k\ge 2$, a {\bf $k$-dense community} of a graph $G$, denoted by $DC_k(G)$, is a maximal connected subgraph of $G$ induced by the vertex set $$V_{DC_k(G)} = \{v\in V(G) : \exists u\in V(G)\ {\rm such\ that\} uv\in E(G)\ {\rm and\} m_{DC_{k(G)}}(uv)\ge k-2\}.$$ In this research, we characterize which graphs are $k$-dense but not $(k+1)$-dense for some values of $k$ and study the minimum and maximum number of edges such graphs can have. A better understanding of $k$-dense sub-graphs (or communities) helps in the study of the connectivity of large complex graphs (or networks) in the real world., Comment: In submission, 16pgs

Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid u \in V(G_1), v \in V(G_2), v=f(u)\}$. A functigraph is a generalization of a \emph{permutation graph} (also known as a \emph{generalized prism}) in the sense of Chartrand and Harary. In this paper, we study domination in functigraphs. Let $\gamma(G)$ denote the domination number of $G$. It is readily seen that $\gamma(G) \le \gamma(C(G,f)) \le 2 \gamma(G)$. We investigate for graphs generally, and for cycles in great detail, the functions which achieve the upper and lower bounds, as well as the realization of the intermediate values., Comment: 18 pages, 8 figures

Given a graph G, its triangular line graph is the graph T(G) with vertex set consisting of the edges of G and adjacencies between edges that are incident in G as well as being within a common triangle. Graphs with a representation as the triangular line graph of some graph G are triangular line graphs, which have been studied under many names including anti-Gallai graphs, 2-in-3 graphs, and link graphs. While closely related to line graphs, triangular line graphs have been difficult to understand and characterize. Van Bang Le asked if recognizing triangular line graphs has an efficient algorithm or is computationally complex. We answer this question by proving that the complexity of recognizing triangular line graphs is NP-complete via a reduction from 3-SAT., Comment: 18 pages, 8 figures, 4 tables