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In network science, the non-homogeneity of node degrees has been a concerned issue for study. Yet, with the modern web technologies today, the traditional social communication topologies have evolved from node-central structures to online cycle-based communities, urgently requiring new network theories and tools. Switching the focus from node degrees to network cycles, it could reveal many interesting properties from the perspective of totally homogeneous networks, or sub-networks in a complex network, especially basic simplexes (cliques) such as links and triangles. Clearly, comparing to node degrees it is much more challenging to deal with network cycles. For studying the latter, a new clique vector space framework is introduced in this paper, where the vector space with a basis consisting of links has the dimension equal to the number of links, that with a basis consisting of triangles has the dimension equal to the number of triangles, and so on. These two vector spaces are related through a boundary operator, e.g., mapping the boundary of a triangle in one space to the sun of three links in the other space. Under the new framework, some important concepts and methodologies from algebraic topology, such as characteristic number, homology group and Betti number, will have a play in network science leading to foreseeable new research directions. As immediate applications, the paper illustrates some important characteristics affecting the collective behaviors of complex networks, some new cycle-dependent importance indexes of nodes, and implications for network synchronization and brain network analysis.
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Multilayer networks allow for modeling complex relationships, where individuals are embedded in multiple social networks at the same time. Given the ubiquity of such relationships, these networks have been increasingly gaining attention in the literature. This paper presents the first analysis of the robustness of centrality measures against strategic manipulation in multilayer networks. More specifically, we consider an evader who strategically chooses which connections to form in a multilayer network in order to obtain a low centrality-based ranking-thereby reducing the chance of being highlighted as a key figure in the network-while ensuring that she remains connected to a certain group of people. We prove that determining an optimal way to hide is NP-complete and hard to approximate for most centrality measures considered in our study. Moreover, we empirically evaluate a number of heuristics that the evader can use. Our results suggest that the centrality measures that are functions of the entire network topology are more robust to such a strategic evader than their counterparts which consider each layer separately.
Recently, Broido & Clauset (2019) mentioned that (strict) Scale-Free networks were rare, in real life. This might be related to the statement of Stumpf, Wiuf & May (2005), that sub-networks of scale-free networks are not scale-free. In the later, those sub-networks are asymptotically scale-free, but one should not forget about second-order deviation (possibly also third order actually). In this article, we introduce a concept of extended scale-free network, inspired by the extended Pareto distribution, that actually is maybe more realistic to describe real network than the strict scale free property. This property is consistent with Stumpf, Wiuf & May (2005): sub-network of scale-free larger networks are not strictly scale-free, but extended scale-free.
With the growing amount of mobile social media, offline ephemeral social networks (OffESNs) are receiving more and more attentions. Offline ephemeral social networks (OffESNs) are the networks created ad-hoc at a specific location for a specific purpose and lasting for short period of time, relying on mobile social media such as Radio Frequency Identification (RFID) and Bluetooth devices. The primary purpose of people in the OffESNs is to acquire and share information via attending prescheduled events. Event Recommendation over this kind of networks can facilitate attendees on selecting the prescheduled events and organizers on making resource planning. However, because of lack of users preference and rating information, as well as explicit social relations, both rating based traditional recommendation methods and social-trust based recommendation methods can no longer work well to recommend events in the OffESNs. To address the challenges such as how to derive users latent preferences and social relations and how to fuse the latent information in a unified model, we first construct two heterogeneous interaction social networks, an event participation network and a physical proximity network. Then, we use them to derive users latent preferences and latent networks on social relations, including like-minded peers, co-attendees and friends. Finally, we propose an LNF (Latent Networks Fusion) model under a pairwise factor graph to infer event attendance probabilities for recommendation. Experiments on an RFID-based real conference dataset have demonstrated the effectiveness of the proposed model compared with typical solutions.
Competition networks are formed via adversarial interactions between actors. The Dynamic Competition Hypothesis predicts that influential actors in competition networks should have a large number of common out-neighbors with many other nodes. We empirically study this idea as a centrality score and find the measure predictive of importance in several real-world networks including food webs, conflict networks, and voting data from Survivor.
The recording and sharing of cooking recipes, a human activity dating back thousands of years, naturally became an early and prominent social use of the web. The resulting online recipe collections are repositories of ingredient combinations and cooking methods whose large-scale and variety yield interesting insights about both the fundamentals of cooking and user preferences. At the level of an individual ingredient we measure whether it tends to be essential or can be dropped or added, and whether its quantity can be modified. We also construct two types of networks to capture the relationships between ingredients. The complement network captures which ingredients tend to co-occur frequently, and is composed of two large communities: one savory, the other sweet. The substitute network, derived from user-generated suggestions for modifications, can be decomposed into many communities of functionally equivalent ingredients, and captures users preference for healthier variants of a recipe. Our experiments reveal that recipe ratings can be well predicted with features derived from combinations of ingredient networks and nutrition information.
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