Evolution characteristics of the network core in the facebook

Statistical properties of the static networks have been extensively studied. However, online social networks are evolving dynamically, understanding the evolving characteristics of the core is one of major concerns in online social networks. In this paper, we empirically investigate the evolving characteristics of the Facebook core. Firstly, we separate the Facebook-link(FL) and Facebook-wall(FW) datasets into 28 snapshots in terms of timestamps. By employing the k-core decomposition method to identify the core of each snapshot, we find that the core sizes of the FL and FW networks approximately contain about 672 and 373 nodes regardless of the exponential growth of the network sizes. Secondly, we analyze evolving topological properties of the core, including the k-core value, assortative coefficient, clustering coefficient and the average shortest path length. Empirical results show that nodes in the core are getting more interconnected in the evolving process. Thirdly, we investigate the life span of nodes belonging to the core. More than 50% nodes stay in the core for more than one year, and 19% nodes always stay in the core from the first snapshot. Finally, we analyze the connections between the core and the whole network, and find that nodes belonging to the core prefer to connect nodes with high k-core values, rather than the high degrees ones. This work could provide new insights into the online social network analysis

Structure and dynamics of core-periphery networks

Recent studies uncovered important core/periphery network structures characterizing complex sets of cooperative and competitive interactions between network nodes, be they proteins, cells, species or humans. Better characterization of the structure, dynamics and function of core/periphery networks is a key step of our understanding cellular functions, species adaptation, social and market changes. Here we summarize the current knowledge of the structure and dynamics of "traditional" core/periphery networks, rich-clubs, nested, bow-tie and onion networks. Comparing core/periphery structures with network modules, we discriminate between global and local cores. The core/periphery network organization lies in the middle of several extreme properties, such as random/condensed structures, clique/star configurations, network symmetry/asymmetry, network assortativity/disassortativity, as well as network hierarchy/anti-hierarchy. These properties of high complexity together with the large degeneracy of core pathways ensuring cooperation and providing multiple options of network flow re-channelling greatly contribute to the high robustness of complex systems. Core processes enable a coordinated response to various stimuli, decrease noise, and evolve slowly. The integrative function of network cores is an important step in the development of a large variety of complex organisms and organizations. In addition to these important features and several decades of research interest, studies on core/periphery networks still have a number of unexplored areas.Comment: a comprehensive review of 41 pages, 2 figures, 1 table and 182 reference

A Network Theoretical Approach to Real-World Problems: Application of the K-Core Algorithm to Various Systems

The study of complex networks is, at its core, an exploration of the mechanisms that control the world in which we live at every scale, from particles no bigger than a grain of sand and amino acids that comprise proteins, to social networks, ecosystems, and even countries. Indeed, we find that, regardless of the physical size of the network\u27s components, we may apply principles of complex network theory, thermodynamics, and statistical mechanics to not only better understand these specific networks, but to formulate theories which may be applied to problems on a more general level. This thesis explores several networks at vastly different scales, ranging from the microscopic (amino acids and frictional packed particles) to the macroscopic (human subjects asked to view a set of videos) to the massive (real ecosystems and the financial ecosystem (Haldane 2011, May 2008) of stocks in the S&P500 stock index). The networks are discussed in chronological order of analysis. We begin with a review of k-core theory, including its applications to certain dynamical systems, as this is an important concept to understand for the next two sections. A discussion of the network structure (specifically, a k-shell decomposition) of both ecological and financial dynamic networks, and the implications of this structure for determining a network\u27s tipping point of collapse, follows. Third, this same k-shell structure is examined for networks of frictional particles approaching a jamming transition, where it is seen that the jamming transition is a k-core transition given by random network theory. Lastly comes a thermodynamical examination of human eye-tracking networks built from data of subjects asked to watch the commercials of the 2014 Super Bowl Game; we determine, using a Maximum Entropy approach, that the collective behavior of this small sample can be used to predict population-wide preferences. The behavior of all of these networks are explained using aspects of network theoretical and statistical mechanics frameworks and can be extended beyond the specific networks analyzed herein

A Structural Analysis of the Internet AS-level topology

The study of the structural characteristics of the Internet topology at the Autonomous System (AS) level of abstraction is an important and interesting subject that has attracted significant interest over the last few years. Above all, a deep knowledge of the Internet underlying structure helps researchers in designing a more accurate model of the network; as a result, engineers can design applications and protocols that can take into account the underlying structure and test their projects on synthetic graphs, thereby developing more efficient algorithms. A significant challenge for researchers analyzing the Internet is how to interpret the global organization of the graph as the coexistence of its structural blocks associated with more highly interconnected parts, namely communities. While a huge number of papers have already been published on the issue of community detection, very little attention has so far been devoted to the discovery and interpretation of Internet communities. The contribution of this work is twofold. First, we study the evolution of the Internet AS-level topology over the last 9 years by means of two innovative approaches: the k-dense method and the dK-analysis. Second, we focus on substructures that play a key role in the Internet connectivity, and we investigate the classes of the ASes and the nature of the connections that create such communities. We find that as the Internet grows over time, some of its structural properties remain unchanged. Although the size of the network, as well as the kMAX -dense index (an index of the maximum level of density reached in a network), has doubled over the last 9 years, we show that after proper normalizations the k-dense decomposition has remained stable. Besides, we provided a clear evidence that the formation of denser and denser sub-graphs over time has been triggered by the proliferation of Internet eXchange Points (IXP) and public peering connections. We found that ASes within most densely-connected substructures are usually Network Service Providers, Content Providers, or Content Delivery Networks; in addition, all of them participate to at least one IXP

Structure-oriented prediction in complex networks

Complex systems are extremely hard to predict due to its highly nonlinear interactions and rich emergent properties. Thanks to the rapid development of network science, our understanding of the structure of real complex systems and the dynamics on them has been remarkably deepened, which meanwhile largely stimulates the growth of effective prediction approaches on these systems. In this article, we aim to review different network-related prediction problems, summarize and classify relevant prediction methods, analyze their advantages and disadvantages, and point out the forefront as well as critical challenges of the field