Mapping the Curricular Structure and Contents of Network Science Courses

As network science has matured as an established field of research, there are already a number of courses on this topic developed and offered at various higher education institutions, often at postgraduate levels. In those courses, instructors adopted different approaches with different focus areas and curricular designs. We collected information about 30 existing network science courses from various online sources, and analyzed the contents of their syllabi or course schedules. The topics and their curricular sequences were extracted from the course syllabi/schedules and represented as a directed weighted graph, which we call the topic network. Community detection in the topic network revealed seven topic clusters, which matched reasonably with the concept list previously generated by students and educators through the Network Literacy initiative. The minimum spanning tree of the topic network revealed typical flows of curricular contents, starting with examples of networks, moving onto random networks and small-world networks, then branching off to various subtopics from there. These results illustrate the current state of consensus formation (including variations and disagreements) among the network science community on what should be taught about networks and how, which may also be informative for K--12 education and informal education.Comment: 17 pages, 11 figures, 2 tables; to appear in Cramer, C. et al. (eds.), Network Science in Education -- Tools and Techniques for Transforming Teaching and Learning (Springer, 2017, in press

Uncovering space-independent communities in spatial networks

Accepted versio

Reachability Problems in Nondeterministic Polynomial Maps on the Integers

We study the reachability problems in various nondeterministic polynomial maps in Zn. We prove that the reachability problem for very simple three-dimensional affine maps (with independent variables) is undecidable and is PSPACE-hard for two-dimensional quadratic maps. Then we show that the complexity of the reachability problem for maps without functions of the form ±x + b is lower. In this case the reachability problem is PSPACE-complete in general, and NP-hard for any fixed dimension. Finally we extend the model by considering maps as language acceptors and prove that the universality problem is undecidable for two-dimensional affine maps

Identifying and Alleviating Concept Drift in Streaming Tensor Decomposition

Tensor decompositions are used in various data mining applications from social network to medical applications and are extremely useful in discovering latent structures or concepts in the data. Many real-world applications are dynamic in nature and so are their data. To deal with this dynamic nature of data, there exist a variety of online tensor decomposition algorithms. A central assumption in all those algorithms is that the number of latent concepts remains fixed throughout the entire stream. However, this need not be the case. Every incoming batch in the stream may have a different number of latent concepts, and the difference in latent concepts from one tensor batch to another can provide insights into how our findings in a particular application behave and deviate over time. In this paper, we define "concept" and "concept drift" in the context of streaming tensor decomposition, as the manifestation of the variability of latent concepts throughout the stream. Furthermore, we introduce SeekAndDestroy, an algorithm that detects concept drift in streaming tensor decomposition and is able to produce results robust to that drift. To the best of our knowledge, this is the first work that investigates concept drift in streaming tensor decomposition. We extensively evaluate SeekAndDestroy on synthetic datasets, which exhibit a wide variety of realistic drift. Our experiments demonstrate the effectiveness of SeekAndDestroy, both in the detection of concept drift and in the alleviation of its effects, producing results with similar quality to decomposing the entire tensor in one shot. Additionally, in real datasets, SeekAndDestroy outperforms other streaming baselines, while discovering novel useful components.Comment: 16 Pages, Accepted at ECML-PKDD 201

Weather-it missions: a social network analysis perspective of an online citizen inquiry community

Citizen inquiry is an innovative informal science learning approach, which engages members of the general public in scientific investigations sparked by their personal experience of everyday science, and to which other members can contribute. This paper aims to describe the network of interactions and contributions of Weather-it, an online Citizen Inquiry community accommodated by the nQuire-it platform, which involves people in creating and maintaining their own weather missions (investigations). The interaction patterns within Weather-it are mainly explored through social network analysis of community members and missions. The results indicate the quiet and active members within the community, their splitting into sub-communities, and their contribution and data collection methods and preferences. These results provide in-sight into the behaviour of people in such public engagement projects

A New Approach to Measuring Distances in Dense Graphs

The problem of computing distances and shortest paths between vertices in graphs is one of the fundamental issues in graph theory. It is of great importance in many different applications, for example, transportation, and social network analysis. However, efficient shortest distance algorithms are still desired in many disciplines. Basically, the majority of dense graphs have ties between the shortest distances. Therefore, we consider a different approach and introduce a new measure to solve all-pairs shortest paths for undirected and unweighted graphs. This measures the shortest distance between any two vertices by considering the length and the number of all possible paths between them. The main aim of this new approach is to break the ties between equal shortest paths SP, which can be obtained by the Breadth-first search algorithm (BFS), and distinguish meaningfully between these equal distances. Moreover, using the new measure in clustering produces higher quality results compared with SP. In our study, we apply two different clustering techniques: hierarchical clustering and K-means clustering, with four different graph models, and for a various number of clusters. We compare the results using a modularity function to check the quality of our clustering results

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

Detecting community structure in social networks is a fundamental problem empowering us to identify groups of actors with similar interests. There have been extensive works focusing on finding communities in static networks, however, in reality, due to dynamic nature of social networks, they are evolving continuously. Ignoring the dynamic aspect of social networks, neither allows us to capture evolutionary behavior of the network nor to predict the future status of individuals. Aside from being dynamic, another significant characteristic of real-world social networks is the presence of leaders, i.e. nodes with high degree centrality having a high attraction to absorb other members and hence to form a local community. In this paper, we devised an efficient method to incrementally detect communities in highly dynamic social networks using the intuitive idea of importance and persistence of community leaders over time. Our proposed method is able to find new communities based on the previous structure of the network without recomputing them from scratch. This unique feature, enables us to efficiently detect and track communities over time rapidly. Experimental results on the synthetic and real-world social networks demonstrate that our method is both effective and efficient in discovering communities in dynamic social networks

Consistency and trends of technological innovations: a network approach to the international patent classification data

Classifying patents by the technology areas they pertain is important to enable information search and facilitate policy analysis and socio-economic studies. Based on the OECD Triadic Patent Family database, this study constructs a cohort network based on the grouping of IPC subclasses in the same patent families, and a citation network based on citations between subclasses of patent families citing each other. This paper presents a systematic analysis approach which obtains naturally formed network clusters identified using a Lumped Markov Chain method, extracts community keys traceable over time, and investigates two important community characteristics: consistency and changing trends. The results are verified against several other methods, including a recent research measuring patent text similarity. The proposed method contributes to the literature a network-based approach to study the endogenous community properties of an exogenously devised classification system. The application of this method may improve accuracy and efficiency of the IPC search platform and help detect the emergence of new technologies

Considerations about multistep community detection

The problem and implications of community detection in networks have raised a huge attention, for its important applications in both natural and social sciences. A number of algorithms has been developed to solve this problem, addressing either speed optimization or the quality of the partitions calculated. In this paper we propose a multi-step procedure bridging the fastest, but less accurate algorithms (coarse clustering), with the slowest, most effective ones (refinement). By adopting heuristic ranking of the nodes, and classifying a fraction of them as `critical', a refinement step can be restricted to this subset of the network, thus saving computational time. Preliminary numerical results are discussed, showing improvement of the final partition.Comment: 12 page