Spectral centrality measures in complex networks

Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank, eigenvector centrality and the hub/authority scores of HITS. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.Comment: 11 pages, 10 figures, 5 tables. Final version published in Physical Review

Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices

We study a disordered classical Heisenberg magnet with uniformly antiferromagnetic interactions which are frustrated on account of their long-range Coulomb form, {\em i.e.} $J(r)\sim -A\ln r$ in $d=2$ and $J(r)\sim A/r$ in $d=3$. This arises naturally as the $T\rightarrow 0$ limit of the emergent interactions between vacancy-induced degrees of freedom in a class of diluted Coulomb spin liquids (including the classical Heisenberg antiferromagnets on checkerboard, SCGO and pyrochlore lattices) and presents a novel variant of a disordered long-range spin Hamiltonian. Using detailed analytical and numerical studies we establish that this model exhibits a very broad paramagnetic regime that extends to very large values of $A$ in both $d=2$ and $d=3$. In $d=2$, using the lattice-Green function based finite-size regularization of the Coulomb potential (which corresponds naturally to the underlying low-temperature limit of the emergent interactions between orphan-spins), we only find evidence that freezing into a glassy state occurs in the limit of strong coupling, $A=\infty$, while no such transition seems to exist at all in $d=3$. We also demonstrate the presence and importance of screening for such a magnet. We analyse the spectrum of the Euclidean random matrices describing a Gaussian version of this problem, and identify a corresponding quantum mechanical scattering problem.Comment: two-column PRB format; 17 pages; 24 .eps figure

Bow-tie structures of twitter discursive communities

Bow-tie structures were introduced to describe the World Wide Web (WWW): in the direct network in which the nodes are the websites and the edges are the hyperlinks connecting them, the greatest number of nodes takes part to a bow-tie, i.e. a Weakly Connected Component (WCC) composed of 3 main sectors: IN, OUT and SCC. SCC is the main Strongly Connected Component of WCC, i.e. the greatest subgraph in which each node is reachable by any other one. The IN and OUT sectors are the set of nodes not included in SCC that, respectively, can access and are accessible to nodes in SCC. In the WWW, the greatest part of the websites can be found in the SCC, while the search engines belong to IN and the authorities, as Wikipedia, are in OUT. In the analysis of Twitter debate, the recent literature focused on discursive communities, i.e. clusters of accounts interacting among themselves via retweets. In the present work, we studied discursive communities in 8 different thematic Twitter datasets in various languages. Surprisingly, we observed that almost all discursive communities therein display a bow-tie structure during political or societal debates. Instead, they are absent when the argument of the discussion is different as sport events, as in the case of Euro2020 Turkish and Italian datasets. We furthermore analysed the quality of the content created in the various sectors of the different discursive communities, using the domain annotation from the fact-checking website Newsguard: we observe that, when the discursive community is affected by m/disinformation, the content with the lowest quality is the one produced and shared in SCC and, in particular, a strong incidence of low- or non-reputable messages is present in the flow of retweets between the SCC and the OUT sectors. In this sense, in discursive communities affected by m/disinformation, the greatest part of the accounts has access to a great variety of contents, but whose quality is, in general, quite low; such a situation perfectly describes the phenomenon of infodemic, i.e. the access to "an excessive amount of information about a problem, which makes it difficult to identify a solution", according to WHO

New business model and local governance in supporting social and environmental solutions: a social network analysis to evaluate the Italian local action group’s “Terra è Vita” role

Current issues, such as climate change and social and economic disparities, are complex and context-dependent, influencing several economic and social actors. Micro-small and medium enterprises that populate rural areas often have lower risks than other companies but less innovation and fewer financial resources and capabilities. Here, a local convenor could help support these enterprises to drive their social, environmental, and economic behaviours to safeguard natural resources, respond to social community needs, and fulfil their economic goals. The European Union’s Community-Led Local Development programme defines local action groups as actors who help develop and grow local areas in social and economic fields. We analyse this role, highlighting that by focusing on social and environmental issues, the convenor can stimulate changes in the traditional business model and the social business model characterised by the business ambidexterity involved in producing economic value that is also relevant to addressing the community’s needs. We study the effectiveness of a local action group in its convenor role for local actors’ behaviours on economic, social, and environmental themes. The study uses social network analysis to extract the network backbone that links 150 local area entrepreneurs according to their perceptions of the local area’s main weaknesses. The results are twofold: they indicate that the local action group is perceived as an effective convenor and that its activities are instrumental in improving local area stakeholders’ performance