Signed networks have long been used to represent social relations of amity (+) and enmity ()
between individuals. Group of individuals who are cyclically connected are said to be …

We show that the chronological removal of cycles from a walk on a graph, known as Lawler's
loop-erasing procedure, generates a preLie co-algebra on the vector space spanned by the …

We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion
statistics in which particles tend to coalesce more than ordinary bosons. We derive the …

A bstract Permutations and associated algebras allow the construction of half and quarter
BPS operators in maximally supersymmetric Yang Mills theory with U (N), SO (N) and Sp (N) …

Imbalance, incoordination, and inter‐regional economic segmentation of the middle and
lower reaches of the Yellow River (MLYR) have brought challenges to high‐quality …

In a recent work we introduced a measure of importance for groups of vertices in a complex
network. This centrality for groups is always between 0 and 1 and induces the eigenvector …

Simple cycles on a digraph form a trace monoid under the rule that two such cycles
commute if and only if they are vertex disjoint. This rule describes the spatial configuration of …

Networks are versatile representations of the interactions between entities in complex
systems. Cycles on such networks represent feedback processes which play a central role in …

Let $ X $ be an infinite graph of bounded degree; eg, the Cayley graph of a free product of
finite groups. If $ G $ is a finite graph covered by $ X $, it is said to be $ X $-Ramanujan if its …

We present an exact formula for enumerating the simple paths between any two vertices of a
graph. Our formula involves the adjacency matrices of the connected induced subgraphs …