Ordered community structure in networks

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have discrete values, but many networks exhibit assortative mixing by some continuous-valued attribute, such as age or geographical location. In such cases, no discrete communities can be identified. We consider how the notion of community structure can be generalized to networks that are based on continuous-valued attributes: in general, a network may contain discrete communities which are ordered according to their attribute values. We propose a method of generating synthetic ordered networks and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.Comment: This is an extended preprint version that includes an extra example: the college football network as an ordered (spatial) network. Further improvements, not included here, appear in the journal version. Original title changed (from "Ordered and continuous community structure in networks") to match journal versio

Analysis and Assembling of Network Structure in Mutualistic Systems

It has been observed that mutualistic bipartite networks have a nested structure of interactions. In addition, the degree distributions associated with the two guilds involved in such networks (e.g. plants & pollinators or plants & seed dispersers) approximately follow a truncated power law. We show that nestedness and truncated power law distributions are intimately linked, and that any biological reasons for such truncation are superimposed to finite size effects . We further explore the internal organization of bipartite networks by developing a self-organizing network model (SNM) that reproduces empirical observations of pollination systems of widely different sizes. Since the only inputs to the SNM are numbers of plant and animal species, and their interactions (i.e., no data on local abundance of the interacting species are needed), we suggest that the well-known association between species frequency of interaction and species degree is a consequence rather than a cause, of the observed network structure.Comment: J. of. Theor. Biology, in pres

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows one to study community structure in a very general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting material. This is the accepted version of the manuscript (the definitive version appeared in Science), with typographical corrections included her

The co-evolution of emotional well-being with weak and strong friendship ties

Social ties are strongly related to well-being. But what characterizes this relationship? This study investigates social mechanisms explaining how social ties affect well-being through social integration and social influence, and how well-being affects social ties through social selection. We hypothesize that highly integrated individuals - those with more extensive and dense friendship networks - report higher emotional well-being than others. Moreover, emotional well-being should be influenced by the well-being of close friends. Finally, well-being should affect friendship selection when individuals prefer others with higher levels of well-being, and others whose well-being is similar to theirs. We test our hypotheses using longitudinal social network and well-being data of 117 individuals living in a graduate housing community. The application of a novel extension of Stochastic Actor-Oriented Models for ordered networks (ordered SAOMs) allows us to detail and test our hypotheses for weak- and strong-tied friendship networks simultaneously. Results do not support our social integration and social influence hypotheses but provide evidence for selection: individuals with higher emotional well-being tend to have more strong-tied friends, and there are homophily processes regarding emotional well-being in strong-tied networks. Our study highlights the two-directional relationship between social ties and well-being, and demonstrates the importance of considering different tie strengths for various social processes

Searching for network modules

When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a novel type of objective function for graph clustering, in the form of a multilinear polynomial whose coefficients are determined by network topology. It may be thought of as a potential function, to be maximized, taking its values on fuzzy clusterings or families of fuzzy subsets of nodes over which every node distributes a unit membership. When suitably parametrized, this potential is shown to attain its maximum when every node concentrates its all unit membership on some module. The output thus is a partition, while the original discrete optimization problem is turned into a continuous version allowing to conceive alternative search strategies. The instance of the problem being a pseudo-Boolean function assigning real-valued cluster scores to node subsets, modularity maximization is employed to exemplify a so-called quadratic form, in that the scores of singletons and pairs also fully determine the scores of larger clusters, while the resulting multilinear polynomial potential function has degree 2. After considering further quadratic instances, different from modularity and obtained by interpreting network topology in alternative manners, a greedy local-search strategy for the continuous framework is analytically compared with an existing greedy agglomerative procedure for the discrete case. Overlapping is finally discussed in terms of multiple runs, i.e. several local searches with different initializations.Comment: 10 page

Community detection with spiking neural networks for neuromorphic hardware

We present results related to the performance of an algorithm for community detection which incorporates event-driven computation. We define a mapping which takes a graph G to a system of spiking neurons. Using a fully connected spiking neuron system, with both inhibitory and excitatory synaptic connections, the firing patterns of neurons within the same community can be distinguished from firing patterns of neurons in different communities. On a random graph with 128 vertices and known community structure we show that by using binary decoding and a Hamming-distance based metric, individual communities can be identified from spike train similarities. Using bipolar decoding and finite rate thresholding, we verify that inhibitory connections prevent the spread of spiking patterns.Comment: Conference paper presented at ORNL Neuromorphic Workshop 2017, 7 pages, 6 figure