157,040 research outputs found
Line graphs as social networks
The line graphs are clustered and assortative. They share these topological
features with some social networks. We argue that this similarity reveals the
cliquey character of the social networks. In the model proposed here, a social
network is the line graph of an initial network of families, communities,
interest groups, school classes and small companies. These groups play the role
of nodes, and individuals are represented by links between these nodes. The
picture is supported by the data on the LiveJournal network of about 8 x 10^6
people. In particular, sharp maxima of the observed data of the degree
dependence of the clustering coefficient C(k) are associated with cliques in
the social network.Comment: 11 pages, 4 figure
Signed graph embedding: when everybody can sit closer to friends than enemies
Signed graphs are graphs with signed edges. They are commonly used to
represent positive and negative relationships in social networks. While balance
theory and clusterizable graphs deal with signed graphs to represent social
interactions, recent empirical studies have proved that they fail to reflect
some current practices in real social networks. In this paper we address the
issue of drawing signed graphs and capturing such social interactions. We relax
the previous assumptions to define a drawing as a model in which every vertex
has to be placed closer to its neighbors connected via a positive edge than its
neighbors connected via a negative edge in the resulting space. Based on this
definition, we address the problem of deciding whether a given signed graph has
a drawing in a given -dimensional Euclidean space. We present forbidden
patterns for signed graphs that admit the introduced definition of drawing in
the Euclidean plane and line. We then focus on the -dimensional case, where
we provide a polynomial time algorithm that decides if a given complete signed
graph has a drawing, and constructs it when applicable
On the equivalence between graph isomorphism testing and function approximation with GNNs
Graph neural networks (GNNs) have achieved lots of success on
graph-structured data. In the light of this, there has been increasing interest
in studying their representation power. One line of work focuses on the
universal approximation of permutation-invariant functions by certain classes
of GNNs, and another demonstrates the limitation of GNNs via graph isomorphism
tests.
Our work connects these two perspectives and proves their equivalence. We
further develop a framework of the representation power of GNNs with the
language of sigma-algebra, which incorporates both viewpoints. Using this
framework, we compare the expressive power of different classes of GNNs as well
as other methods on graphs. In particular, we prove that order-2 Graph
G-invariant networks fail to distinguish non-isomorphic regular graphs with the
same degree. We then extend them to a new architecture, Ring-GNNs, which
succeeds on distinguishing these graphs and provides improvements on real-world
social network datasets
Segregation in Networks.
Schelling (1969, 1971a,b, 1978) considered a simple model with individual agents who only care about the types of people living in their own local neighborhood. The spatial structure was represented by a one- or two-dimensional lattice. Schelling showed that an integrated society will generally unravel into a rather segregated one even though no individual agent strictly prefers this. We make a first step to generalize the spatial proximity model to a proximity model of segregation. That is, we examine models with individual agents who interact ’locally’ in a range of network structures with topological properties that are different from those of regular lattices. Assuming mild preferences about with whom they interact, we study best-response dynamics in random and regular non-directed graphs as well as in small-world and scale-free networks. Our main result is that the system attains levels of segregation that are in line with those reached in the lattice-based spatial proximity model. In other words, mild proximity preferences can explain segregation not just in regular spatial networks but also in more general social networks. Furthermore, segregation levels do not dramatically vary across different network structures. That is, Schelling’s original results seem to be robust also to the structural properties of the network.Spatial proximity model, Social segregation, Schelling, Proximity preferences, Social networks, Undirected graphs, Best-response dynamics.
Segregation in Networks
Schelling (1969, 1971, 1971, 1978) considered a simple model with individual agents who only care about the types of people living in their own local neighborhood. The spatial structure was represented by a one- or two-dimensional lattice. Schelling showed that an integrated society will generally unravel into a rather segregated one even though no individual agent strictly prefers this. We make a first step to generalize the spatial proximity model to a proximity model of segregation. That is, we examine models with individual agents who interact 'locally' in a range of network structures with topological properties that are different from those of regular lattices. Assuming mild preferences about with whom they interact, we study best-response dynamics in random and regular non-directed graphs as well as in small-world and scale-free networks. Our main result is that the system attains levels of segregation that are in line with those reached in the lattice-based spatial proximity model. In other words, mild proximity preferences can explain segregation not just in regular spatial networks but also in more general social networks. Furthermore, segregation levels do not dramatically vary across different network structures. That is, Schelling's original results seem to be robust also to the structural properties of the network.Spatial proximity model, Social segregation, Schelling, Proximity preferences, Social networks, Undirected graphs, Best-response dynamics.
Tracing the Use of Practices through Networks of Collaboration
An active line of research has used on-line data to study the ways in which
discrete units of information---including messages, photos, product
recommendations, group invitations---spread through social networks. There is
relatively little understanding, however, of how on-line data might help in
studying the diffusion of more complex {\em practices}---roughly, routines or
styles of work that are generally handed down from one person to another
through collaboration or mentorship. In this work, we propose a framework
together with a novel type of data analysis that seeks to study the spread of
such practices by tracking their syntactic signatures in large document
collections. Central to this framework is the notion of an "inheritance graph"
that represents how people pass the practice on to others through
collaboration. Our analysis of these inheritance graphs demonstrates that we
can trace a significant number of practices over long time-spans, and we show
that the structure of these graphs can help in predicting the longevity of
collaborations within a field, as well as the fitness of the practices
themselves.Comment: To Appear in Proceedings of ICWSM 2017, data at
https://github.com/CornellNLP/Macro
Models for On-line Social Networks
On-line social networks such as Facebook or Myspace are of increasing interest to computer scientists, mathematicians, and social scientists alike. In such real-world networks, nodes represent people and edges represent friendships between them. Mathematical models have been proposed for a variety of complex real-world networks such as the web graph, but relatively few models exist for on-line social networks.
We present two new models for on-line social networks: a deterministic model we call Iterated Local Transitivity (ILT), and a random ILT model. We study various properties in the deterministic ILT model such as average degree, average distance, and diameter. We show that the domination number and cop number stay the same no matter how many nodes or edges are added over time. We investigate the automorphism groups and eigenvalues of graphs generated by the ILT model. We show that the random ILT model follows a power-law degree distribution and we provide a theorem about the power law exponent of this model. We present simulations for the degree distribution of the random ILT model
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