17 research outputs found
Visualizing Structural Balance in Signed Networks
Network visualization has established as a key complement to network analysis
since the large variety of existing network layouts are able to graphically
highlight different properties of networks. However, signed networks, i.e.,
networks whose edges are labeled as friendly (positive) or antagonistic
(negative), are target of few of such layouts and none, to our knowledge, is
able to show structural balance, i.e., the tendency of cycles towards including
an even number of negative edges, which is a well-known theory for studying
friction and polarization.
In this work we present Structural-balance-viz: a novel visualization method
showing whether a connected signed network is balanced or not and, in the
latter case, how close the network is to be balanced. Structural-balance-viz
exploits spectral computations of the signed Laplacian matrix to place
network's nodes in a Cartesian coordinate system resembling a balance (a
scale). Moreover, it uses edge coloring and bundling to distinguish positive
and negative interactions. The proposed visualization method has
characteristics desirable in a variety of network analysis tasks:
Structural-balance-viz is able to provide indications of balance/polarization
of the whole network and of each node, to identify two factions of nodes on the
basis of their polarization, and to show their cumulative characteristics.
Moreover, the layout is reproducible and easy to compare.
Structural-balance-viz is validated over synthetic-generated networks and
applied to a real-world dataset about political debates confirming that it is
able to provide meaningful interpretations
Analyzing and Visualizing American Congress Polarization and Balance with Signed Networks
Signed networks and balance theory provide a natural setting for real-world
scenarios that show polarization dynamics, positive/negative relationships, and
political partisanships. For example, they have been proven effective for
studying the increasing polarization of the votes in the two chambers of the
American Congress from World War II on.
To provide further insights into this particular case study, we propose the
application of a framework to analyze and visualize a signed graph's
configuration based on the exploitation of the corresponding Laplacian matrix'
spectral properties. The overall methodology is comparable with others based on
the frustration index, but it has at least two main advantages: first, it
requires a much lower computational cost; second, it allows for a quantitative
and visual assessment of how arbitrarily small subgraphs (even single nodes)
contribute to the overall balance (or unbalance) of the network.
The proposed pipeline allows to explore the polarization dynamics shown by
the American Congress from 1945 to 2020 at different resolution scales. In
fact, we are able to spot and to point out the influence of some (groups of)
congressmen in the overall balance, as well as to observe and explore
polarization's evolution of both chambers across the years
Dynamical Stability of Threshold Networks over Undirected Signed Graphs
In this paper we study the dynamic behavior of threshold networks on
undirected signed graphs. While much attention has been given to the
convergence and long-term behavior of this model, an open question remains: How
does the underlying graph structure influence network dynamics? While similar
papers have been carried out for threshold networks (as well as for other
networks) these have largely focused on unsigned networks. However, the signed
graph model finds applications in various real-world domains like gene
regulation and social networks.
By studying a graph parameter that we call "stability index," we search to
establish a connection between the structure and the dynamics of threshold
network. Interestingly, this parameter is related to the concepts of
frustration and balance in signed graphs. We show that graphs that present
negative stability index exhibit stable dynamics, meaning that the dynamics
converges to fixed points regardless of threshold parameters. Conversely, if at
least one subgraph has positive stability index, oscillations in long term
behavior may appear. Finally, we generalize the analysis to network dynamics
under periodic update schemes and we explore the case in which the stability
index is positive for some subgraph finding that attractors with
superpolynomial period on the size of the network may appear
Unpacking polarization: Antagonism and Alignment in Signed Networks of Online Interaction
Online polarization research currently focuses on studying single-issue
opinion distributions or computing distance metrics of interaction network
structures. Limited data availability often restricts studies to positive
interaction data, which can misrepresent the reality of a discussion. We
introduce a novel framework that aims at combining these three aspects, content
and interactions, as well as their nature (positive or negative), while
challenging the prevailing notion of polarization as an umbrella term for all
forms of online conflict or opposing opinions. In our approach, built on the
concepts of cleavage structures and structural balance of signed social
networks, we factorize polarization into two distinct metrics: Antagonism and
Alignment. Antagonism quantifies hostility in online discussions, based on the
reactions of users to content. Alignment uses signed structural information
encoded in long-term user-user relations on the platform to describe how well
user interactions fit the global and/or traditional sides of discussion. We can
analyse the change of these metrics through time, localizing both relevant
trends but also sudden changes that can be mapped to specific contexts or
events. We apply our methods to two distinct platforms: Birdwatch, a US
crowd-based fact-checking extension of Twitter, and DerStandard, an Austrian
online newspaper with discussion forums. In these two use cases, we find that
our framework is capable of describing the global status of the groups of users
(identification of cleavages) while also providing relevant findings on
specific issues or in specific time frames. Furthermore, we show that our four
metrics describe distinct phenomena, emphasizing their independent
consideration for unpacking polarization complexities