Network and Graph...
Follow
576 views | +0 today
 
Scooped by Bernard Ryefield
onto Network and Graph Theory
Scoop.it!

Exactly scale-free scale-free networks

There is mounting evidence of the apparent ubiquity of scale-free networks among complex systems. Many natural and physical systems exhibit patterns of interconnection that conform, approximately, to the structure expected of a scale-free network. We propose an efficient algorithm to generate representative samples from the space of all networks defined by a particular (scale-free) degree distribution. Using this algorithm we are able to systematically explore that space with some surprising results: in particular, we find that preferential attachment growth models do not yield typical realizations and that there is a certain latent structure among such networks --- which we loosely term "hub-centric". We provide a method to generate or remove this latent hub-centric bias --- thereby demonstrating exactly which features of preferential attachment networks are atypical of the broader class of scale free networks. Based on these results we are also able to statistically determine whether experimentally observed networks are really typical realizations of a given degree distribution (scale-free degree being the example which we explore). In so doing we propose a surrogate generation method for complex networks, exactly analogous the the widely used surrogate tests of nonlinear time series analysis.

more...
No comment yet.
Your new post is loading...
Your new post is loading...
Rescooped by Bernard Ryefield from Complexity - Complex Systems Theory
Scoop.it!

Global Civil Unrest: Contagion, Self-Organization, and Prediction

Global Civil Unrest: Contagion, Self-Organization, and Prediction | Network and Graph Theory | Scoop.it

Civil unrest is a powerful form of collective human dynamics, which has led to major transitions of societies in modern history. The study of collective human dynamics, including collective aggression, has been the focus of much discussion in the context of modeling and identification of universal patterns of behavior. In contrast, the possibility that civil unrest activities, across countries and over long time periods, are governed by universal mechanisms has not been explored. Here, records of civil unrest of 170 countries during the period 1919–2008 are analyzed. It is demonstrated that the distributions of the number of unrest events per year are robustly reproduced by a nonlinear, spatially extended dynamical model, which reflects the spread of civil disorder between geographic regions connected through social and communication networks. The results also expose the similarity between global social instability and the dynamics of natural hazards and epidemics.

 

 

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Multilayer networks

Multilayer networks | Network and Graph Theory | Scoop.it

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such ‘multilayer’ features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize ‘traditional’ network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other and provide a thorough discussion that compares, contrasts and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Online Social Networks: Threats and Solutions

Many online social network (OSN) users are unaware of the numerous security risks that exist in these networks, including privacy violations, identity theft, and sexual harassment, just to name a few. According to recent studies, OSN users readily expose personal and private details about themselves, such as relationship status, date of birth, school name, email address, phone number, and even home address. This information, if put into the wrong hands, can be used to harm users both in the virtual world and in the real world. These risks become even more severe when the users are children. In this paper we present a thorough review of the different security and privacy risks which threaten the well-being of OSN users in general, and children in particular. In addition, we present an overview of existing solutions that can provide better protection, security, and privacy for OSN users. We also offer simple-to-implement recommendations for OSN users which can improve their security and privacy when using these platforms. Furthermore, we suggest future research directions.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

The Strange Evolution of Self Obsession on Reddit — The Physics arXiv Blog — Medium

The Strange Evolution of Self Obsession on Reddit — The Physics arXiv Blog — Medium | Network and Graph Theory | Scoop.it
The self-proclaimed frontpage of the internet has grown exponentially in just a few years.
more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Human Genome Variation and the Concept of Genotype Networks

Human Genome Variation and the Concept of Genotype Networks | Network and Graph Theory | Scoop.it
PLOS ONE: an inclusive, peer-reviewed, open-access resource from the PUBLIC LIBRARY OF SCIENCE. Reports of well-performed scientific studies from all disciplines freely available to the whole world.
more...
No comment yet.
Suggested by Samir
Scoop.it!

ECCS 2014 Living Satellite

ECCS 2014 Living Satellite | Network and Graph Theory | Scoop.it

Workshop on Robustness, Adaptability and Critical Transitions in Living Systems.Call for papers http://seis.bristol.ac.uk/~fs13378/eccs_2014_livingsys.html

 

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Influence Spread in Social Networks: A Study via a Fluid Limit of the Linear Threshold Model

Threshold based models have been widely used in characterizing collective behavior on social networks. An individual's threshold indicates the minimum level of influence that must be exerted, by other members of the population engaged in some activity, before the individual will join the activity. In this work, we begin with a homogeneous version of the Linear Threshold model proposed by Kempe et al. in the context of viral marketing, and generalize this model to arbitrary threshold distributions. We show that the evolution can be modeled as a discrete time Markov chain, and, by using a certain scaling, we obtain a fluid limit that provides an ordinary differential equation model (o.d.e.). We find that the threshold distribution appears in the o.d.e. via its hazard rate function. We demonstrate the accuracy of the o.d.e. approximation and derive explicit expressions for the trajectory of influence under the uniform threshold distribution. Also, for an exponentially distributed threshold, we show that the fluid dynamics are equivalent to the well-known SIR model in epidemiology. We also numerically study how other hazard functions (obtained from the Weibull and loglogistic distributions) provide qualitative different characteristics of the influence evolution, compared to traditional epidemic models, even in a homogeneous setting. We finally show how the model can be extended to a setting with multiple communities and conclude with possible future directions.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

AnaVANET: an experiment and visualization tool for vehicular networks

AnaVANET: an experiment and visualization tool for vehicular networks | Network and Graph Theory | Scoop.it
The experimental evaluation of wireless and mobile networks is a challenge that rarely substitutes simulation in research works.
more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

How Community Feedback Shapes User Behavior

Social media systems rely on user feedback and rating mechanisms for personalization, ranking, and content filtering. However, when users evaluate content contributed by fellow users (e.g., by liking a post or voting on a comment), these evaluations create complex social feedback effects. This paper investigates how ratings on a piece of content affect its author's future behavior. By studying four large comment-based news communities, we find that negative feedback leads to significant behavioral changes that are detrimental to the community. Not only do authors of negatively-evaluated content contribute more, but also their future posts are of lower quality, and are perceived by the community as such. Moreover, these authors are more likely to subsequently evaluate their fellow users negatively, percolating these effects through the community. In contrast, positive feedback does not carry similar effects, and neither encourages rewarded authors to write more, nor improves the quality of their posts. Interestingly, the authors that receive no feedback are most likely to leave a community. Furthermore, a structural analysis of the voter network reveals that evaluations polarize the community the most when positive and negative votes are equally split.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Spatial Neural Networks and their Functional Samples: Similarities and Differences

Models of neural networks have proven their utility in the development of learning algorithms in computer science and in the theoretical study of brain dynamics in computational neuroscience. We propose in this paper a spatial neural network model to analyze the important class of functional networks, which are commonly employed in computational studies of clinical brain imaging time series. We developed a simulation framework inspired by multichannel brain surface recordings (more specifically, EEG -- electroencephalogram) in order to link the mesoscopic network dynamics (represented by sampled functional networks) and the microscopic network structure (represented by an integrate-and-fire neural network located in a 3D space -- hence the term spatial neural network). Functional networks are obtained by computing pairwise correlations between time-series of mesoscopic electric potential dynamics, which allows the construction of a graph where each node represents one time-series. The spatial neural network model is central in this study in the sense that it allowed us to characterize sampled functional networks in terms of what features they are able to reproduce from the underlying spatial network. Our modeling approach shows that, in specific conditions of sample size and edge density, it is possible to precisely estimate several network measurements of spatial networks by just observing functional samples.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Together we stand, Together we fall, Together we win: Dynamic Team Formation in Massive Open Online Courses

Massive Open Online Courses (MOOCs) offer a new scalable paradigm for e-learning by providing students with global exposure and opportunities for connecting and interacting with millions of people all around the world. Very often, students work as teams to effectively accomplish course related tasks. However, due to lack of face to face interaction, it becomes difficult for MOOC students to collaborate. Additionally, the instructor also faces challenges in manually organizing students into teams because students flock to these MOOCs in huge numbers. Thus, the proposed research is aimed at developing a robust methodology for dynamic team formation in MOOCs, the theoretical framework for which is grounded at the confluence of organizational team theory, social network analysis and machine learning. A prerequisite for such an undertaking is that we understand the fact that, each and every informal tie established among students offers the opportunities to influence and be influenced. Therefore, we aim to extract value from the inherent connectedness of students in the MOOC. These connections carry with them radical implications for the way students understand each other in the networked learning community. Our approach will enable course instructors to automatically group students in teams that have fairly balanced social connections with their peers, well defined in terms of appropriately selected qualitative and quantitative network metrics.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

A signature of power law network dynamics

Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two simple graph parameters--the logarithm of the average cluster size and logarithm of the ratio of the edges of the graph to the theoretically maximum number of edges for that graph--that holds for all growing power law graphs. The result establishes a novel property of evolving power-law networks in the asymptotic limit of network size. Numerical simulations as well as fitting to real-world citation co-authorship networks demonstrate that the result holds for networks of finite sizes, and provides a convenient measure of the extent to which an evolving family of networks belongs to the same power-law class.

more...
No comment yet.
Rescooped by Bernard Ryefield from Complexity - Complex Systems Theory
Scoop.it!

Behavioral and Network Origins of Wealth Inequality: Insights from a Virtual World

Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on wealth could so far not be inferred from data. Here we study wealth data from the virtual economy of the massive multiplayer online game (MMOG) Pardus. This data not only contains every player's wealth at every point in time, but also all actions of every player over a timespan of almost a decade. We find that wealth distributions in the virtual world are very similar to those in western countries. In particular we find an approximate exponential for low wealth and a power-law tail. The Gini index is found to be 0.65, which is close to the indices of many Western countries. We find that wealth-increase rates depend on the time when players entered the game. Players that entered the game early on tend to have remarkably higher wealth-increase rates than those who joined later. Studying the players' positions within their social networks, we find that the local position in the trade network is most relevant for wealth. Wealthy people have high in- and out-degree in the trade network, relatively low nearest-neighbor degree and a low clustering coefficient. Wealthy players have many mutual friendships and are socially well respected by others, but spend more time on business than on socializing. We find that players that are not organized within social groups with at least three members are significantly poorer on average. We observe that high `political' status and high wealth go hand in hand. Wealthy players have few personal enemies, but show animosity towards players that behave as public enemies.

more...
Eli Levine's curator insight, April 5, 7:53 AM

When you let laissez-faire take its course, only a few individuals really end up on top.  That's not to say that markets shouldn't be allowed and enabled to exist, for the sake of the free exchange of goods, services, knowledge, wealth, etc.  It is saying that we need non-intrusive mechanisms to help make sure that the wealth that is produced is enjoyed by everyone who produced it.

 

Some people will always have more than others, for behavioral reasons and for circumstantial reasons.  That is not a problem, in my own view.  The problem comes, for me, when their focus on wealth becomes so great that they lose sight of their human needs on the individual as well as social and environmental levels, such that they choose wealth that they will not use over that which they need for survival and physical/psychological well being.

 

It's a form of being disconnected with the real world, kind of like schizophrenia.  The brain isn't functioning properly when  greed is and has taken over, for one reason or another.  It should be considered a mental illness that we could, potentially in time, treat, such that these individuals who are not aware and do not care to be aware of their actual place in the universe can lead normal, happy, healthy and appropriately placed lives in our societies.

 

So, we're left with the present situation in which work is undervalued, relative to what it produces, while executive management is way overvalued relative to its healthy role in the economy and society.  I'm not saying that pure equality is desirable, because sometimes people do work harder than others and deserve a greater share of wealth than someone who didn't work when they honestly could have.  What I'm saying, is that indulging the elite's fantasy of the ego is detrimental to themselves and to others, and that I don't think it should be accepted or tolerated within our social world.

 

If you want equality of opportunities, you must have more equality of outcomes.  That is yet another fact about our world that conservatives fail to accept and appreciate, if they're attempting to realize a world in which we are all together as one, rather than a world where we are heavily stratified according to an artificial hierarchy.  That is the difference between a conservative and a progressive.  One wants us all to be living together in peace, harmony, stability and, for want of a better word, love, while the other just wants everyone in a specific place according to birth.  One promotes democracy and inclusivity, the other, discourages it.  One works better for humanity on the tangible level, the other, does not.

 

And it's just a difference in brain type/values that makes them be something so antithetical to what Western civilization has stood for.

 

Think about it.

Scooped by Bernard Ryefield
Scoop.it!

Network Effects on Scientific Collaborations

Network Effects on Scientific Collaborations | Network and Graph Theory | Scoop.it

Measures of social network analysis, for example network centrality and tie strength, have been utilized extensively in current co-authorship literature to explore different behavioural patterns of co-authorship networks. Using three SNA measures (i.e., degree centrality, closeness centrality and betweenness centrality), we explore scientific collaboration networks to understand factors influencing performance (i.e., citation count) and formation (tie strength between authors) of such networks. A citation count is the number of times an article is cited by other articles. We use co-authorship dataset of the research field of ‘steel structure’ for the year 2005 to 2009. To measure the strength of scientific collaboration between two authors, we consider the number of articles co-authored by them. In this study, we examine how citation count of a scientific publication is influenced by different centrality measures of its co-author(s) in a co-authorship network. We further analyze the impact of the network positions of authors on the strength of their scientific collaborations. We use both correlation and regression methods for data analysis leading to statistical validation. We identify that citation count of a research article is positively correlated with the degree centrality and betweenness centrality values of its co-author(s). Also, we reveal that degree centrality and betweenness centrality values of authors in a co-authorship network are positively correlated with the strength of their scientific collaborations.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

The Social Network of Alexander the Great: Social Network Analysis in Ancient History

The Social Network of Alexander the Great: Social Network Analysis in Ancient History | Network and Graph Theory | Scoop.it
The Social Network of Alexander the Great: Social Network Analysis in Ancient History
more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Information, Meaning, and Intellectual Organization in Networks of Inter-Human Communication

The Shannon-Weaver model of linear information transmission is extended with two loops potentially generating redundancies: (i) meaning is provided locally to the information from the perspective of hindsight, and (ii) meanings can be codified differently and then refer to other horizons of meaning. Thus, three layers are distinguished: variations in the communications, historical organization at each moment of time, and evolutionary self-organization of the codes of communication over time. Furthermore, the codes of communication can functionally be different and then the system is both horizontally and vertically differentiated. All these subdynamics operate in parallel and necessarily generate uncertainty. However, meaningful information can be considered as the specific selection of a signal from the noise; the codes of communication are social constructs that can generate redundancy by giving different meanings to the same information. Reflexively, one can translate among codes in more elaborate discourses. The second (instantiating) layer can be operationalized in terms of semantic maps using the vector space model; the third in terms of mutual redundancy among the latent dimensions of the vector space. Using Blaise Cronin's {\oe}uvre, the different operations of the three layers are demonstrated empirically.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Rising Tides or Rising Stars?: Dynamics of Shared Attention on Twitter during Media Events

Rising Tides or Rising Stars?: Dynamics of Shared Attention on Twitter during Media Events | Network and Graph Theory | Scoop.it
PLOS ONE: an inclusive, peer-reviewed, open-access resource from the PUBLIC LIBRARY OF SCIENCE. Reports of well-performed scientific studies from all disciplines freely available to the whole world.
more...
No comment yet.
Rescooped by Bernard Ryefield from Complexity - Complex Systems Theory
Scoop.it!

▶ Large-Scale Structure in Networks - YouTube

▶ Large-Scale Structure in Networks - YouTube | Network and Graph Theory | Scoop.it
Mark Newman May 2, 2014 Annual Science Board Symposium and Meeting Complexity: Theory and Practice
more...
Eli Levine's curator insight, June 8, 11:40 PM

To know the structure is to know a HUMONGOUS part of the function and, thus, the ability to predict.  It seems to me to be a large fractal pattern of clusters, nodes and connections (but, that is just in my relatively uneducated eye). 

 

Never forget, though, that there are important qualitative aspects to networks (think of defacto qualities of the nodes, groups of nodes and the connections amongst them).  Very important for social and/or ecological/causal relation networks (essentially, a network that outlines and maps accurately the function of a system and all of the flows of information and material resources).

 

Really cool stuff here.

 

Think about it..

Scooped by Bernard Ryefield
Scoop.it!

Predicting Successful Memes using Network and Community Structure v2

We investigate the predictability of successful memes using their early spreading patterns in the underlying social networks. We propose and analyze a comprehensive set of features and develop an accurate model to predict future popularity of a meme given its early spreading patterns. Our paper provides the first comprehensive comparison of existing predictive frameworks. We categorize our features into three groups: influence of early adopters, community concentration, and characteristics of adoption time series. We find that features based on community structure are the most powerful predictors of future success. We also find that early popularity of a meme is not a good predictor of its future popularity, contrary to common belief. Our methods outperform other approaches, particularly in the task of detecting very popular or unpopular memes.

more...
No comment yet.
Rescooped by Bernard Ryefield from Complexity - Complex Systems Theory
Scoop.it!

Shock waves on complex networks

Shock waves on complex networks | Network and Graph Theory | Scoop.it
Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a cascading way and affect a significant fraction of the network. Almost discontinuous perturbations can be modeled by shock waves which can eventually interfere constructively and endanger the normal functionality of the infrastructure. We study their dynamics by solving the Burgers equation under random perturbations on several real and artificial directed graphs. Even for graphs with a narrow distribution of node properties (e.g., degree or betweenness), a steady state is reached exhibiting a heterogeneous load distribution, having a difference of one order of magnitude between the highest and average loads. Unexpectedly we find for the European power grid and for finite Watts-Strogatz networks a broad pronounced bimodal distribution for the loads. To identify the most vulnerable nodes, we introduce the concept of node-basin size, a purely topological property which we show to be strongly correlated to the average load of a node.

Via Shaolin Tan, NESS, Bernard Ryefield
more...
Eli Levine's curator insight, May 20, 5:19 AM

Indeed, this is intuitive enough without the mathematics to back it up.  This could be mapped out and used for prioritizing the defense or attack of various points within the network, either in the digital or analog worlds.

 

Way cool science!

 

Think about it.

Rescooped by Bernard Ryefield from Papers
Scoop.it!

Modeling dynamics of attention in social media with user efficiency

Evolution of online social networks is driven by the need of their members to share and consume content, resulting in a complex interplay between individual activity and attention received from others. In a context of increasing information overload and limited resources, discovering which are the most successful behavioral patterns to attract attention is very important. To shed light on the matter, we look into the patterns of activity and popularity of users in the Yahoo Meme microblogging service. We observe that a combination of different type of social and content-producing activity is necessary to attract attention and the efficiency of users, namely the average attention received per piece of content published, for many users has a defined trend in its temporal footprint. The analysis of the user time series of efficiency shows different classes of users whose different activity patterns give insights on the type of behavior that pays off best in terms of attention gathering. In particular, sharing content with high spreading potential and then supporting the attention raised by it with social activity emerges as a frequent pattern for users gaining efficiency over time.

 

Modeling dynamics of attention in social media with user efficiency
Carmen Vaca Ruiz, Luca Maria Aiello and Alejandro Jaimes

EPJ Data Science 2014, 3:5  http://dx.doi.org/10.1140/epjds30


Via Complexity Digest
more...
No comment yet.
Rescooped by Bernard Ryefield from Papers
Scoop.it!

Measuring Large-Scale Social Networks with High Resolution

Measuring Large-Scale Social Networks with High Resolution | Network and Graph Theory | Scoop.it

This paper describes the deployment of a large-scale study designed to measure human interactions across a variety of communication channels, with high temporal resolution and spanning multiple years—the Copenhagen Networks Study. Specifically, we collect data on face-to-face interactions, telecommunication, social networks, location, and background information (personality, demographics, health, politics) for a densely connected population of 1 000 individuals, using state-of-the-art smartphones as social sensors. Here we provide an overview of the related work and describe the motivation and research agenda driving the study. Additionally, the paper details the data-types measured, and the technical infrastructure in terms of both backend and phone software, as well as an outline of the deployment procedures. We document the participant privacy procedures and their underlying principles. The paper is concluded with early results from data analysis, illustrating the importance of multi-channel high-resolution approach to data collection.

 

Measuring Large-Scale Social Networks with High Resolution

Stopczynski A, Sekara V, Sapiezynski P, et al.

PLoS ONE 9(4): e95978 (2014)

http://dx.doi.org/10.1371/journal.pone.0095978


Via Complexity Digest
more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Layer aggregation and reducibility of multilayer interconnected networks

Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, with thousands of protein-protein interactions each. A fundamental open question is then how much information is really necessary to accurately represent the structure of a multilayer complex system, and if and when some of the layers can indeed be aggregated. Here we introduce a method, based on information theory, to reduce the number of layers in multilayer networks, while minimizing information loss. We validate our approach on a set of synthetic benchmarks, and prove its applicability to an extended data set of protein-genetic interactions, showing cases where a strong reduction is possible and cases where it is not. Using this method we can describe complex systems with an optimal trade--off between accuracy and complexity.

more...
No comment yet.
Scooped by Bernard Ryefield
Scoop.it!

Dynamics of Information Spreading in Online Social Networks

Online social networks (OSNs) are changing the way information spreads throughout the Internet. A deep understanding of information spreading in OSNs leads to both social and commercial benefits. In this paper, dynamics of information spreading (e.g., how fast and widely the information spreads against time) in OSNs are characterized, and a general and accurate model based on Interactive Markov Chains (IMCs) and mean-field theory is established. This model shows tight relations between network topology and information spreading in OSNs, e.g., the information spreading ability is positively related to the heterogeneity of degree distributions whereas negatively related to the degree-degree correlations in general. Further, the model is extended to feature the time-varying user behavior and the ever-changing information popularity. By leveraging the mean-field theory, the model is able to characterize the complicated information spreading process (e.g., the dynamic patterns of information spreading) with six parameters. Extensive evaluations based on Renren's data set illustrate the accuracy of the model, e.g., it can characterize dynamic patterns of video sharing in Renren precisely and predict future spreading dynamics successfully.

Bernard Ryefield's insight:
updated Apr 24 : http://arxiv.org/abs/1404.5562v2
more...
Rescooped by Bernard Ryefield from Papers
Scoop.it!

Network Weirdness: Exploring the Origins of Network Paradoxes

Social networks have many counter-intuitive properties, including the "friendship paradox" that states, on average, your friends have more friends than you do. Recently, a variety of other paradoxes were demonstrated in online social networks. This paper explores the origins of these network paradoxes. Specifically, we ask whether they arise from mathematical properties of the networks or whether they have a behavioral origin. We show that sampling from heavy-tailed distributions always gives rise to a paradox in the mean, but not the median. We propose a strong form of network paradoxes, based on utilizing the median, and validate it empirically using data from two online social networks. Specifically, we show that for any user the majority of user's friends and followers have more friends, followers, etc. than the user, and that this cannot be explained by statistical properties of sampling. Next, we explore the behavioral origins of the paradoxes by using the shuffle test to remove correlations between node degrees and attributes. We find that paradoxes for the mean persist in the shuffled network, but not for the median. We demonstrate that strong paradoxes arise due to the assortativity of user attributes, including degree, and correlation between degree and attribute.

 

Network Weirdness: Exploring the Origins of Network Paradoxes
Farshad Kooti, Nathan O. Hodas, Kristina Lerman

http://arxiv.org/abs/1403.7242


Via Complexity Digest
more...
António F Fonseca's curator insight, April 10, 5:06 AM

Some network insights into the vague notion of popularity.