Uncovering nodes that spread information between communities in social networks

From many datasets gathered in online social networks, well defined community structures have been observed. A large number of users participate in these networks and the size of the resulting graphs poses computational challenges. There is a particular demand in identifying the nodes responsible for information flow between communities; for example, in temporal Twitter networks edges between communities play a key role in propagating spikes of activity when the connectivity between communities is sparse and few edges exist between different clusters of nodes. The new algorithm proposed here is aimed at revealing these key connections by measuring a node's vicinity to nodes of another community. We look at the nodes which have edges in more than one community and the locality of nodes around them which influence the information received and broadcasted to them. The method relies on independent random walks of a chosen fixed number of steps, originating from nodes with edges in more than one community. For the large networks that we have in mind, existing measures such as betweenness centrality are difficult to compute, even with recent methods that approximate the large number of operations required. We therefore design an algorithm that scales up to the demand of current big data requirements and has the ability to harness parallel processing capabilities. The new algorithm is illustrated on synthetic data, where results can be judged carefully, and also on a real, large scale Twitter activity data, where new insights can be gained

Line Graphs of Weighted Networks for Overlapping Communities

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an alternative, valuable representation of the system's topology, and are shown to have important applications in community detection, as the usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities. We apply it to the analysis of different social and geographical networks.Comment: 8 Pages. New title and text revisions to emphasise differences from earlier paper

Fundamental structures of dynamic social networks

Social systems are in a constant state of flux with dynamics spanning from minute-by-minute changes to patterns present on the timescale of years. Accurate models of social dynamics are important for understanding spreading of influence or diseases, formation of friendships, and the productivity of teams. While there has been much progress on understanding complex networks over the past decade, little is known about the regularities governing the micro-dynamics of social networks. Here we explore the dynamic social network of a densely-connected population of approximately 1000 individuals and their interactions in the network of real-world person-to-person proximity measured via Bluetooth, as well as their telecommunication networks, online social media contacts, geo-location, and demographic data. These high-resolution data allow us to observe social groups directly, rendering community detection unnecessary. Starting from 5-minute time slices we uncover dynamic social structures expressed on multiple timescales. On the hourly timescale, we find that gatherings are fluid, with members coming and going, but organized via a stable core of individuals. Each core represents a social context. Cores exhibit a pattern of recurring meetings across weeks and months, each with varying degrees of regularity. Taken together, these findings provide a powerful simplification of the social network, where cores represent fundamental structures expressed with strong temporal and spatial regularity. Using this framework, we explore the complex interplay between social and geospatial behavior, documenting how the formation of cores are preceded by coordination behavior in the communication networks, and demonstrating that social behavior can be predicted with high precision.Comment: Main Manuscript: 16 pages, 4 figures. Supplementary Information: 39 pages, 34 figure

How to suppress undesired synchronization

It is delightful to observe the emergence of synchronization in the blinking of fireflies to attract partners and preys. Other charming examples of synchronization can also be found in a wide range of phenomena such as, e.g., neurons firing, lasers cascades, chemical reactions, and opinion formation. However, in many situations the formation of a coherent state is not pleasant and should be mitigated. For example, the onset of synchronization can be the root of epileptic seizures, traffic congestion in communication networks, and the collapse of constructions. Here we propose the use of contrarians to suppress undesired synchronization. We perform a comparative study of different strategies, either requiring local or total knowledge of the system, and show that the most efficient one solely requires local information. Our results also reveal that, even when the distribution of neighboring interactions is narrow, significant improvement in mitigation is observed when contrarians sit at the highly connected elements. The same qualitative results are obtained for artificially generated networks as well as two real ones, namely, the Routers of the Internet and a neuronal network

Finding communities in sparse networks

Spectral algorithms based on matrix representations of networks are often used to detect communities but classic spectral methods based on the adjacency matrix and its variants fail to detect communities in sparse networks. New spectral methods based on non-backtracking random walks have recently been introduced that successfully detect communities in many sparse networks. However, the spectrum of non-backtracking random walks ignores hanging trees in networks that can contain information about the community structure of networks. We introduce the reluctant backtracking operators that explicitly account for hanging trees as they admit a small probability of returning to the immediately previous node unlike the non-backtracking operators that forbid an immediate return. We show that the reluctant backtracking operators can detect communities in certain sparse networks where the non-backtracking operators cannot while performing comparably on benchmark stochastic block model networks and real world networks. We also show that the spectrum of the reluctant backtracking operator approximately optimises the standard modularity function similar to the flow matrix. Interestingly, for this family of non- and reluctant-backtracking operators the main determinant of performance on real-world networks is whether or not they are normalised to conserve probability at each node.Comment: 11 pages, 4 figure

Maximal entropy random walk in community finding

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study encompasses the use of the stochastic matrix of a random walk, its mean first-passage time matrix, and a matrix of weighted paths count. We briefly indicate the connection between those quantities and propose substituting the maximal-entropy random walk for the previously chosen models. This unique random walk maximises the entropy of ensembles of paths of given length and endpoints, which results in equiprobability of those paths. We compare performance of the selected algorithms on LFR benchmark graphs. The results show that the change in performance depends very strongly on the particular algorithm, and can lead to slight improvements as well as significant deterioration.Comment: 7 pages, 4 figures, submitted to European Physical Journal Special Topics following the 4-th Conference on Statistical Physics: Modern Trends and Applications, July 3-6, 2012 Lviv, Ukrain

Coupled effects of local movement and global interaction on contagion

By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we investigate the coupled effects of random walk and intragroup interaction on contagion. Compared with the situation where only local movement or individual-based linkage exists, the coexistence of them leads to a wider spread of infectious disease. The roles of narrowing segregated spatial domain and reducing mobility in epidemic control are checked, these two measures are found to be conducive to curbing the spread of infectious disease. Considering heterogeneous time scales between local movement and global interaction, a log-log relation between the change in the number of infected individuals and the timescale $\tau$ is found. A theoretical analysis indicates that the evolutionary dynamics in the present model is related to the encounter probability and the encounter time. A functional relation between the epidemic threshold and the ratio of shortcuts, and a functional relation between the encounter time and the timescale $\tau$ are found