Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session K43: Complex Networks and their Applications IUndergraduate

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Sponsoring Units: GSNP Chair: Flaviano Morone, City College of New York Room: 346 
Wednesday, March 16, 2016 8:00AM  8:12AM 
K43.00001: Influence maximization in complex networks through optimal percolation Flaviano Morone, Hernan Makse The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network, or, if immunized, would prevent the diffusion of a large scale epidemic. Localizing this optimal, that is, minimal, set of structural nodes, called influencers, is one of the most important problems in network science. Here we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a manybody system, where the form of the interactions is fixed by the nonbacktracking matrix of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly connected nodes emerges among the optimal influencers. Reference: F. Morone, H. A. Makse, Nature 524,6568 (2015) [Preview Abstract] 
Wednesday, March 16, 2016 8:12AM  8:24AM 
K43.00002: Collective opinion formation on fluctuating networks Vudtiwat Ngampruetikorn, Greg Stephens Thanks to the advent of online social networks, not only are we more connected than ever but we are also able to design and maintain our own social networks. An insight into this phenomenon will be key to understanding modern societies. To this end, we argue that active network maintenance exposes individuals to selective exposure (preference for agreeing information sources) and we explore how this could affect the structure of social networks and collective opinion formation. More technically, we investigate opinion dynamics on a complex network with fast stochastic rewiring. We show that selective exposure while inducing segregation of agents with different opinions, stabilises consensus state regardless of opinion update rules. We argue further that selective exposure can lead to a shorter time to consensus. The time to consensus has nontrivial dependence on the magnitude of selective exposure. Moreover, we find for some opinion updating rules, selective exposure can increase the lifetime of opinion segregation (polarisation of opinions). [Preview Abstract] 
Wednesday, March 16, 2016 8:24AM  8:36AM 
K43.00003: Choice Shift in Opinion Network Dynamics Michael Gabbay Choice shift is a phenomenon associated with small group dynamics whereby group discussion causes group members to shift their opinions in a more extreme direction so that the mean postdiscussion opinion exceeds the mean prediscussion opinion. Also known as group polarization, choice shift is a robust experimental phenomenon and has been wellstudied within social psychology. In opinion network models, shifts toward extremism are typically produced by the presence of stubborn agents at the extremes of the opinion axis, whose opinions are much more resistant to change than moderate agents. However, we present a model in which choice shift can arise without the assumption of stubborn agents; the model evolves member opinions and uncertainties using coupled nonlinear differential equations. In addition, we briefly describe the results of a recent experiment conducted involving online group discussion concerning the outcome of National Football League games are described. The model predictions concerning the effects of network structure, disagreement level, and team choice (favorite or underdog) are in accord with the experimental results. [Preview Abstract] 
Wednesday, March 16, 2016 8:36AM  8:48AM 
K43.00004: Social Network Influence and Personal Financial Status Shaojun Luo, Flaviano Morone, Carlos Sarraute, Hernan Makse Networks of social ties emerging from individual economic needs display a highly structured architecture. In response to socioeconomic demands, people reshape their circle of contacts for maximizing their social status, and ipso facto, the pattern of their interconnections is strongly correlates with their personal financial situation. In this work we transform this qualitative and verbal statement into an operative definition, which allows us to quantify the economic wellness of individuals trough a measure of their collective influence. We consider the network of mobile phone calls made by the Mexican population during three months, in order to study the correlation of person's economic situation with her network location. Notably, we find that rich people tend to be also the most influential nodes, i.e., they selforganize to optimally position themselves in the network. This finding may be also raised at the level of a principle, a fact that would explain the emergence of the phenomenon of collective influence itself as the result of the local optimization of socioeconomic interactions. Our method represents a powerful and efficient indicator of socioeconomic robustness, which may be applied to maximize the effect of large scale economic intervention and stimulus policies [Preview Abstract] 
Wednesday, March 16, 2016 8:48AM  9:00AM 
K43.00005: More Opportunities than Wealth: Inequality and Emergent Social Classes in a Network of Power and Frustration Cristiano Nisoli, Benoit Mahault, Avadh Saxena We introduce a minimal agentbased model to qualitatively conceptualize the allocation of limited wealth among more abundant opportunities. There the interplay of power, satisfaction and frustration determines the distribution, concentration, and inequality of wealth. Our framework allows us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, lawofthejungle setting, where every agent can acquire wealth from, or lose wealth to, anybody else invariably leads to large inequality. The picture is however dramatically modified when hard constraints are imposed over agents, and they are limited to share wealth with neighbors on a network. We address dynamical societies via an out of equilibrium coevolution {\it of} the network, driven by a competition between power and frustration. The ratio between power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of the indices of equality. In particular, it leads to the emergence of three selforganized social classes, lower, middle, and upper class, whose interactions drive a cyclical regime. [Preview Abstract] 
Wednesday, March 16, 2016 9:00AM  9:12AM 
K43.00006: Dynamic networks community detection via low rank component recovery of adjacency matrices Wei Bao, George Michailidis Dynamic community detection in networks has been of high interest due to its various applications. In this work, we apply low rank extraction technique on adjacency matrices to approximate the community structures. Not only can we accurately identify the phase transition time points where significant changes in the community structures occur, but also we can increase the accuracy of the core community structures recovered in the ‘peace’ time ranges by averaging the low rank components. A systematic methodology has been proposed as how to accomplish the target. Factor model, and stochastic block model (including weighted scenario) have been tested for the robustness of our model. Besides, applications on both Kuramoto model and US Senate Roll Call data are also carried out and interesting results are obtained. [Preview Abstract] 
Wednesday, March 16, 2016 9:12AM  9:24AM 
K43.00007: Multiway spectral community detection in networks Xiao Zhang, Mark Newman Spectral methods are widely used for community detection in networks because of their high efficiency and amenability to formal analysis. However, spectral algorithms have been limited to the division of networks into only two or three communities. Here we present a spectral algorithm that can directly divide a network into any number of communities. The algorithm makes use of a mapping from modularity maximization to a vector partitioning problem, combined with a fast heuristic for vector partitioning. We compare the performance of this spectral algorithm with previous approaches and find it to give superior results. We also give demonstrative applications of the algorithm to realworld networks and find that it produces results in good agreement with expectations for the networks studied. [Preview Abstract] 
Wednesday, March 16, 2016 9:24AM  9:36AM 
K43.00008: Utilizing Maximal Independent Sets as Dominating Sets in ScaleFree Networks N. Derzsy, F. Molnar Jr., B. K. Szymanski, G. Korniss Dominating sets provide key solution to various critical problems in networked systems, such as detecting, monitoring, or controlling the behavior of nodes. Motivated by graph theory literature [Erdos, \textit{Israel J. Math.} \textbf{4}, 233 (1966)], we studied \textit{maximal independent sets} (MIS) as dominating sets in scalefree networks. We investigated the scaling behavior of the size of MIS in artificial scalefree networks with respect to multiple topological properties (size, average degree, powerlaw exponent, assortativity), evaluated its resilience to network damage resulting from random failure or targeted attack [Molnar et al., \textit{Sci. Rep.} \textbf{5}, 8321 (2015)], and compared its efficiency to previously proposed dominating set selection strategies. We showed that, despite its small set size, MIS provides very high resilience against network damage. Using extensive numerical analysis on both synthetic and realworld (social, biological, technological) network samples, we demonstrate that our method effectively satisfies four essential requirements of dominating sets for their practical applicability on largescale realworld systems: 1.) small set size, 2.) minimal network information required for their construction scheme, 3.) fast and easy computational implementation, and 4.) resiliency to network damage. [Preview Abstract] 
Wednesday, March 16, 2016 9:36AM  9:48AM 
K43.00009: Growing Networks with Positive and Negative Links Corynne Dech, Shadrack Antwi, Leah Shaw Scalefree networks grown via preferential attachment have been used to model realworld networks such as the Internet, citation networks, and social networks. Here we investigate signed scalefree networks where an edge represents a positive or negative connection. We present analytic results and simulation for a growing signed network model. We compare the signed network to an unsigned scalefree network. We discuss several options for preferential attachment in a signed network that could be further adapted to model the accumulation of links over time in realworld signed networks. [Preview Abstract] 
Wednesday, March 16, 2016 9:48AM  10:00AM 
K43.00010: Robustness of networks of networks with degreedegree correlation Byungjoon Min, Santiago Canals, Hernan Makse Many realworld complex systems ranging from critical infrastructure and transportation networks to living systems including brain and cellular networks are not formed by an isolated network but by a network of networks. Randomly coupled networks with interdependency between different networks may easily result in abrupt collapse. Here, we seek a possible explanation of stable functioning in natural networks of networks including functional brain networks. Specifically, we analyze the robustness of networks of networks focused on onetomany interconnections between different networks and degreedegree correlation. Implication of the network robustness on functional brain networks of rats is also discussed. [Preview Abstract] 
Wednesday, March 16, 2016 10:00AM  10:12AM 
K43.00011: Degree distributions of bipartite networks and their projections Demival Vasques Filho, Dion O'Neale Bipartite networks play an important role in the analysis of social and economic systems as they explicitly show the conceptual links between different types of entities. As an example, it is possible to build networks to investigate interactions regarding scientific and technological innovation that are well represented by a natural bipartite structure. Since we are often most interested in only one of the node types (e.g. the authors in an authorpublication network), it is common to end up working with a projected version of the underlying bipartite network. The topology of projections and the dynamics that take place on it are highly dependent on the probability distribution of nodes degrees. We use the formalism of generating functions to infer how the degree distributions of the original bipartite network affect the distribution in the projected version. Moreover, we create artificial bipartite graphs by arbitrarily choosing degree distributions for the sets of nodes and construct the projection to analyze the resulting probability distribution. Our findings show that when projecting onto a particular set of nodes, the resulting degree distribution follows the behavior of the probability distribution of such nodes, subject, however, to the tail of the opposite distribution. [Preview Abstract] 
(Author Not Attending)

K43.00012: Spectra of Adjacency Matrices in Networks with Extreme Introverts and Extroverts Kevin E. Bassler, Royce K.P. Zia In recent studies of networks with preferred degrees (suitable for describing social networks in which individuals tend to prefer a certain number of contacts), the XIE model of extreme introverts and extroverts was found to display remarkable collective behavior and to raise interesting theoretical issues. Though this system is defined through its dynamics, i.e., introverts/extroverts always cut/add links, the steady state turns out to be a Boltzmannlike distribution. While the intragroup links are static, the crosslinks are dynamic and lead to an ensemble of bipartite graphs, with extraordinary longranged correlations between elements of the incidence matrix (details in JSTAT P07013, 2015). Here, we report simulation studies of a different perspective of networks, namely, the spectra associated with this ensemble of adjacency matrices.~ As a baseline, we first consider the spectra associated with (the adjacency matrices of) a simple random (Erd\^{o}sR\`{e}nyi) ensemble of bipartite graphs, where simulation results can be understood analytically. [Preview Abstract] 
Wednesday, March 16, 2016 10:24AM  10:36AM 
K43.00013: Complex root networks of Chinese characters PoHan Lee, JiaLing Chen, PoCheng Wang, TingTing Chi, ZhiRen Xiao, ZihJian Jhang, YeongNan Yeh, YihYuh Chen, ChinKun Hu There are several sets of Chinese characters still available today, including Oracle Bone Inscriptions (OBI) in Shang Dynasty, Chu characters (CC) used in Chu of Warring State Period, Small Seal Script in dictionary Shuowen Jiezi (SJ) in Eastern Han Dynasty, and Kangxi Dictionary (KD) in Qing Dynasty. Such as Chinese characters were all constructed via combinations of meaningful patterns, called roots. Our studies for the complex networks of all roots indicate that the roots of the characters in OBI, CC, SJ and KD have characteristics of small world networks and scalefree networks. [Preview Abstract] 
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