Degree distribution models are incredibly important tools for analyzing and understanding the structure and formation of social networks, and can help guide the design of efficient graph algorithms. In particular, the Power-law degree distribution has long been used to model the structure of online social networks, and is the basis for algorithms and heuristics in graph applications such as inf...

Email viruses constitute one of the major Internet security problems. In this paper we present an email virus model that accounts for the behaviors of email users, such as email checking frequency and the probability of opening an email attachment. Email viruses spread over a logical network defined by email address books. The topology of email network plays an important role in determining the...

It is widely believed that the Internet’s AS-graph degree distribution obeys a power-law form. Most of the evidence showing the power-law distribution is based on BGP data. However, it was recently argued that since BGP collects data in a tree-like fashion, it only produces a sample of the degree distribution, and this sample may be biased. This argument was backed by simulation data and mathem...

Recently, graph data has been increasingly used in many areas such as bio-informatics and social networks, and a large amount of graph data is generated in those areas. As such, we need to manage such data efficiently. A basic, common problem in graph-related applications is to find graph data that contains a query (Graph Query Problem). However, since examining graph data sequentially incurs a...

The strong power graph G(G) of a group G with elements {1, 2, . . . , n} is a simple graph whose vertices being the elements of G and two distinct vertices i and j are adjacent in G(G) if im1 = jm2 for some positive integers m1,m2 < n. In this paper atfirst we define the strong power graphs and then study some of its properties. Further, we characterise power graphs and strong power graphs and ...

The problem of monitoring an electric power system is placing as few measurement devices as possible. In graph theoretical representation, it can be considered as a variant of domination problem, namely, power domination problem. This problem is to find a minimum power domination set S of a graph G = (V,E) with S ⊆ V and S can dominate all vertices and edges through the observation rules accord...

We propose new evolutionary stochastic models for the web graph and other massive networks, where edges are deleted over time and an edge is chosen to be deleted with probability inversely proportional to the in-degree of the destination. The degree distributions of graphs generated by our models follow a power law. A rigorous proof of power law degree distributions is given using martingales a...