We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

We introduce a system for sensing complex social systems with data collected from 100 mobile phones over the course of 9 months. We demonstrate the ability to use standard Bluetooth-enabled mobile telephones to measure information access and use in different contexts, recognize social patterns in daily user activity, infer relationships, identify socially significant locations, and model organizational rhythms.

/pdf/reality-mining-sensing-complex-social-systems-2gf3rdnw3x.pdf

Reality mining: sensing complex social systems

National Institute of Standards and Technology における超伝導研究及び生活

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems In many cases, however, the edges are not continuously active As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts In some cases, edges are active for non-negligible periods of time: eg, the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

Temporal Networks

The popularity of IEEE 802.11 WLANs has led to dense deployments in urban areas. High density leads to sub-optimal performance unless the interfering networks learn how to optimally use and share the spectrum. This paper proposes two fully distributed algorithms that allow (i) multiple interfering 802.11 access points to select their operating frequency in order to minimize interference, and (ii) users to choose the access point they attach to, in order to get their fair share of the whole network bandwidth. The proposed algorithms rely on Gibbs sampler, and do not require explicit coordination among the wireless devices. They only require the participating wireless nodes to measure local quantities such as interference and transmission delay. The algorithms are shown to lead to optimal bandwidth sharing, where optimality is defined according to the minimal potential delay. We analytically prove the convergence of the proposed algorithms, and study their performance by simulation.

/pdf/measurement-based-self-organization-of-interfering-802-11-4q2c3uz70y.pdf

Measurement-Based Self Organization of Interfering 802.11 Wireless Access Networks

Pocket Switched Networks (PSN) make use of both human mobility and local/global connectivity in order to transfer data between mobile users’ devices. This falls under the Delay Tolerant Networking (DTN) space, focusing on the use of opportunistic networking. One key problem in PSN is in designing forwarding algorithms which cope with human mobility patterns. We present an experiment measuring forty-one humans’ mobility at the Infocom 2005 conference. The results of this experiment are similar to our previous experiments in corporate and academic working environments, in exhibiting a power-law distribution for the time between node contacts. We then discuss the implications of these results on the design of forwarding algorithms for PSN.

/pdf/pocket-switched-networks-real-world-mobility-and-its-1jiqru4o0d.pdf

Pocket Switched Networks: Real-world mobility and its consequences for opportunistic forwarding

CRAWDAD dataset cambridge/haggle (v.2009-05-29)

Online news domains increasingly rely on social media to drive traffic to their websites. Yet we know surprisingly little about how a social media conversation mentioning an online article actually generates clicks. Sharing behaviors, in contrast, have been fully or partially available and scrutinized over the years. While this has led to multiple assumptions on the diffusion of information, each assumption was designed or validated while ignoring actual clicks. We present a large scale, unbiased study of social clicks---that is also the first data of its kind---gathering a month of web visits to online resources that are located in 5 leading news domains and that are mentioned in the third largest social media by web referral (Twitter). Our dataset amounts to 2.8 million shares, together responsible for 75 billion potential views on this social media, and 9.6 million actual clicks to 59,088 unique resources. We design a reproducible methodology and carefully correct its biases. As we prove, properties of clicks impact multiple aspects of information diffusion, all previously unknown:(i) Secondary resources, that are not promoted through headlines and are responsible for the long tail of content popularity, generate more clicks both in absolute and relative terms; (ii) Social media attention is actually long-lived, in contrast with temporal evolution estimated from shares or receptions; (iii) The actual influence of an intermediary or a resource is poorly predicted by their share count, but we show how that prediction can be made more precise.

https://hal.inria.fr/hal-01281190/document

Social Clicks: What and Who Gets Read on Twitter?

Portable devices have more data storage and increasing communication capabilities everyday. In addition to classic infrastructure based communication, these devices can exploit human mobility and opportunistic contacts to communicate. We analyze the characteristics of such opportunistic forwarding paths. We establish that opportunistic mobile networks in general are characterized by a small diameter, a destination device is reachable using only a small number of relays under tight delay constraint. This property is first demonstrated analytically on a family of mobile networks which follow a random graph process. We then establish a similar result empirically with four data sets capturing human mobility, using a new methodology to efficiently compute all the paths that impact the diameter of an opportunistic mobile networks. We complete our analysis of network diameter by studying the impact of intensity of contact rate and contact duration. This work is, to our knowledge, the first validation that the so called "small world" phenomenon applies very generally to opportunistic networking between mobile nodes.

/pdf/the-diameter-of-opportunistic-mobile-networks-22d1sx6wto.pdf

Augustin Chaintreau

Papers

Measurement-Based Self Organization of Interfering 802.11 Wireless Access Networks

Pocket Switched Networks: Real-world mobility and its consequences for opportunistic forwarding

CRAWDAD dataset cambridge/haggle (v.2009-05-29)

Social Clicks: What and Who Gets Read on Twitter?

The diameter of opportunistic mobile networks