Related papers: Ensemble nonequivalence in random graphs with modu…
For a random graph subject to a topological constraint, the microcanonical ensemble requires the constraint to be met by every realisation of the graph (`hard constraint'), while the canonical ensemble requires the constraint to be met only…
Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy of the two ensembles. In [3]…
For random systems subject to a constraint, the microcanonical ensemble requires the constraint to be met by every realisation ("hard constraint"), while the canonical ensemble requires the constraint to be met only on average ("soft…
In this paper we consider a random graph on which topological restrictions are imposed, such as constraints on the total number of edges, wedges, and triangles. We work in the dense regime, in which the number of edges per vertex scales…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…
Two ensembles are often used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is said that breaking of ensemble equivalence (BEE) occurs when…
In [18] we analysed a simple undirected random graph subject to constraints on the total number of edges and the total number of triangles. We considered the dense regime in which the number of edges per vertex is proportional to the number…
Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion,…
The asymptotic equivalence of canonical and microcanonical ensembles is a central concept in statistical physics, with important consequences for both theoretical research and practical applications. However, this property breaks down under…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
We discover a first-order phase transition in the canonical ensemble of random unlabeled networks with a prescribed average number of links. The transition is caused by the nonconcavity of microcanonical entropy. Above the critical point…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
We calculate explicit formulae for the Shannon entropies of several families of tailored random graph ensembles for which no such formulae were as yet available, in leading orders in the system size. These include bipartite graph ensembles…
In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…
The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the…
While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision.…
Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we…
Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…